2,492 results
Search Results
52. Monotonicity and Liouville type theorems of solutions to fully nonlinear fractional problems in the half space.
- Author
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Cheng, Tingzhi and Xu, Xianghui
- Subjects
LIOUVILLE'S theorem ,NONLINEAR equations ,MAXIMUM principles (Mathematics) ,NONLINEAR operators - Abstract
This paper mainly deals with the monotonicity and Liouville type theorems of nonnegative solutions for a class of fully nonlinear fractional equations in half-space. Compared with serial works in [9,14,20], the restrictions on the monotonicity of nonlinear terms and the decay assumption on solutions are not necessary here. Moreover, the monotonicity result of nonnegative bounded solutions for corresponding cooperative systems is also derived. Specifically, we establish some new types of maximum principles for fully nonlinear fractional equations and systems in unbounded domains, which will play crucial roles in carrying on the method of moving planes. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
53. Error estimates for simplified Levenberg–Marquardt method for nonlinear ill-posed operator equations in Hilbert Spaces.
- Author
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Mahale, Pallavi and Kumar, Ankush
- Subjects
- *
NONLINEAR operators , *HILBERT space , *INVERSE problems , *REAL numbers , *OPERATOR equations , *NONLINEAR equations - Abstract
In this paper, we consider the simplified Levenberg–Marquardt method for nonlinear ill-posed inverse problems in Hilbert spaces for obtaining stable approximations of solutions to the ill-posed nonlinear equations of the form F ( u ) = y {F(u)=y} , where F : 풟 ( F ) ⊂ 햴 → 햸 {F:\mathcal{D}(F)\subset\mathsf{U}\to\mathsf{Y}} is a nonlinear operator between Hilbert spaces 햴 {\mathsf{U}} and 햸 {\mathsf{Y}} . The method is defined as follows: u n + 1 δ = u n δ - ( T 0 ∗ T 0 + α n I ) - 1 T 0 ∗ ( F ( u n δ ) - y δ ) , u_{n+1}^{\delta}=u_{n}^{\delta}-(T_{0}^{\ast}T_{0}+\alpha_{n}I)^{-1}T_{0}^{% \ast}(F(u_{n}^{\delta})-y^{\delta}), where T 0 = F ′ ( u 0 ) {T_{0}=F^{\prime}(u_{0})} and T 0 ∗ = F ′ ( u 0 ) ∗ {T_{0}^{\ast}=F^{\prime}(u_{0})^{\ast}} . Here F ′ ( u 0 ) {F^{\prime}(u_{0})} denotes the Frèchet derivative of
F at an initial guess u 0 ∈ 풟 ( F ) {u_{0}\in\mathcal{D}(F)} for the exact solution u † {u^{\dagger}} , F ′ ( u 0 ) ∗ {F^{\prime}(u_{0})^{\ast}} is the adjoint of F ′ ( u 0 ) {F^{\prime}(u_{0})} and { α n } {\{\alpha_{n}\}} is an a priori chosen sequence of non-negative real numbers satisfying suitable properties. We use Morozov-type stopping rule to terminate the iterations. Under suitable non-linearity conditions on operatorF , we show convergence of the method and also obtain a convergence rate result under a Hölder-type source condition on the element u 0 - u † {u_{0}-u^{\dagger}} . Furthermore, we derive convergence of the method for the case when no source conditions are used and the study concludes with numerical examples which validate the theoretical conclusions. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
- View/download PDF
54. Properties of a quasi-uniformly monotone operator and its application to the electromagnetic p-curl systems.
- Author
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Song, Chang-Ho, Ri, Yong-Gon, and Sin, Cholmin
- Subjects
NONLINEAR operators ,OPERATOR equations ,NONLINEAR equations - Abstract
In this paper we propose a new concept of quasi-uniform monotonicity weaker than the uniform monotonicity which has been developed in the study of nonlinear operator equation Au = b. We prove that if A is a quasi-uniformly monotone and hemi-continuous operator, then A
−1 is strictly monotone, bounded and continuous, and thus the Galerkin approximations converge. Also we show an application of a quasi-uniformly monotone and hemi-continuous operator to the proof of the well-posedness and convergence of Galerkin approximations to the solution of steady-state electromagnetic p-curl systems. [ABSTRACT FROM AUTHOR]- Published
- 2022
- Full Text
- View/download PDF
55. Research on Some Problems for Nonlinear Operators in the Z-Z-B Space.
- Author
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Liu, Yiping and Zhu, Chuanxi
- Subjects
NONLINEAR operators ,FIXED point theory ,NONLINEAR equations ,OPERATOR equations - Abstract
In this paper, we first propose a new concept of Z-Z-B spaces, which is a generalization of Z-C-X spaces. Meanwhile, the new concept of the superior cone is introduced. Secondly, we study some new problems for semi-closed 1-set-contractive operators in the Z-Z-B space and obtain some new results. These new theorems are proven by combining partial order theory with fixed point index theory. Regarding these theorems, in the latter part of the paper, the proofs are omitted since the methods of proving these theorems are similar. Moreover, two important inequality lemmas are proven. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
56. Constructing model of nonlinear operators with three-dimensional matrices.
- Author
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Masharipov, S. and Eshniyozov, A.
- Subjects
VOLTERRA operators ,MATHEMATICAL analysis ,FUNCTIONAL analysis ,MATRICES (Mathematics) ,PROBABILITY theory ,NONLINEAR operators ,TWENTIETH century - Abstract
The main goal is to study nonlinear operators and find majorization for operators. Especially, Volterra operators are very important for us. This article has given a three-dimensional matrix and some properties nonlinear operators. Nonlinear operators from matrices are used, and trajectories are founded. The theory of boundary properties made considerable advances in the 20th century, owing to the work of several scientists; it resumed its rapid advance in the second half of that century, accompanied by the appearance of new ideas and methods, novel directions, and objects of study. This class also studied Lyubich. He found some results, but bistochastic operators have not opened yet. This all works related to quadratic stochastic operators. Three-dimensional matrices P
ijk for us to study theories and research of some problems are very important. We use them to study quadratic stochastic operators and relate them to majorization. The main connection between them is as follows: V (x) ≺ x where V(x) operator called Volterra operator. The operator is written as follows: (V x) = ∑ i = 1 m P i j , k x i x j This article gave some properties for majorization and showed some connection with nonlinear operators. The article also gave some examples for nonlinear operators. The main goal is to find an operator and a corresponding matrix that satisfies the definition of majorization. This paper used the theory of majorization and some classes. This article's main result is, constructs nonlinear operators. It is also shown that the operators are bistochastic. The initial points are given from the simplex, and the result shows whether the operator belongs to the simplex or not. The theory of boundary properties made considerable advances in the 20th century, owing to the work of several scientists; it resumed its rapid advance in the second half of that century, accompanied by the appearance of new ideas and methods, novel directions, and objects of study. Its development is closely connected with various fields of mathematical analysis and mathematics in general, first and foremost with probability theory, the theory of real functional analysis, the theory of majorization, and Volterra operators. On the other hand, one of the main purposes of this article is to connect with the Volterra operators. The theory of boundary properties of majorization, which grew out of the works of the Moscow Mathematical School (G.G.Hardy, D.E.Littlewood), was developed in the further works of E. Beccenbach and R.Belman as well as in the works of and other Russian scientists. We will extend this class by constructing a nonlinear operators class for the Volterra operators. Not everything goes exactly without an analog. In such cases, calculations are carried out in other ways. [ABSTRACT FROM AUTHOR]- Published
- 2023
- Full Text
- View/download PDF
57. Decay estimates for the time-fractional evolution equations with time-dependent coefficients.
- Author
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Smadiyeva, Asselya G. and Torebek, Berikbol T.
- Subjects
NONLINEAR evolution equations ,NONLINEAR operators ,NONLINEAR equations ,OPERATOR equations ,POROUS materials ,EVOLUTION equations - Abstract
In this paper, the initial-boundary value problems for the time-fractional degenerate evolution equations are considered. Firstly, in the linear case, we obtain the optimal rates of decay estimates of the solutions. The decay estimates are also established for the time-fractional evolution equations with nonlinear operators such as: p-Laplacian, the porous medium operator, degenerate operator, mean curvature operator and Kirchhoff operator. At the end, some applications of the obtained results are given to derive the decay estimates of global solutions for the time-fractional Fisher-KPP-type equation and the time-fractional porous medium equation with the nonlinear source. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
58. Liouville type theorem for weak solutions of nonlinear system for Grushin operator.
- Author
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Wang, Xinjing
- Subjects
LIOUVILLE'S theorem ,NONLINEAR systems ,NONLINEAR operators ,INTEGRAL inequalities - Abstract
In this paper, we prove Liouville type theorem of positive weak solution of nonlinear system for Grushin operator. We give some integral inequalities, which combine the method of moving plane with the integral inequality to get the result for nonlinear system. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
59. Periodic Homogenization of the Principal Eigenvalue of Second-Order Elliptic Operators.
- Author
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Dávila, Gonzalo, Rodríguez-Paredes, Andrei, and Topp, Erwin
- Subjects
EIGENVALUES ,NONLINEAR operators ,ASYMPTOTIC homogenization ,ELLIPTIC operators ,NONLINEAR equations ,EIGENFUNCTIONS ,ELLIPTIC equations - Abstract
In this paper we investigate homogenization results for the principal eigenvalue problem associated to 1-homogeneous, uniformly elliptic, second-order operators. Under rather general assumptions, we prove that the principal eigenpair associated to an oscillatory operator converges to the eigenpair associated to the effective one. This includes the case of fully nonlinear operators. Rates of convergence for the eigenvalues are provided for linear and nonlinear problems, under extra regularity/convexity assumptions. Finally, a linear rate of convergence (in terms of the oscillation parameter) of suitably normalized eigenfunctions is obtained for linear problems. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
60. The nonlinear superposition operators between some analytic function spaces.
- Author
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Sun, Fangmei and Wulan, Hasi
- Subjects
NONLINEAR operators ,FUNCTION spaces ,ANALYTIC functions ,ANALYTIC spaces ,INTEGRAL functions - Abstract
In this paper we characterize the nonlinear superposition operators mapping the space \mathcal {Q}_s into the Dirichlet-type space \mathcal {D}^p_\alpha and answer basically the remaining open cases provided by Galanopoulos, Girela, and Auxiliadora Márquez [J. Math. Anal. Appl. 463 (2018), pp. 659–680]. Meanwhile, we give some sufficient-necessary conditions for the superposition operators between \mathcal {Q}_s spaces in all cases. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
61. Geraghty–Pata–Suzuki-Type Proximal Contractions and Related Coincidence Best Proximity Point Results.
- Author
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Saleem, Naeem, Raazzia, Maneesha Tur, Hussain, Nawab, and Asiri, Asim
- Subjects
COINCIDENCE ,METRIC spaces ,SYMMETRIC spaces ,NONLINEAR operators ,OPERATOR theory ,CONTRACTIONS (Topology) - Abstract
The objective of this research paper is to establish the existence and uniqueness of the best proximity and coincidence with best proximity point results, specifically focusing on Geraghty–Pata–Suzuki-type proximal mappings. To achieve this, we introduce three types of mappings, all within the context of a complete metric space: an α - θ - Geraghty–Pata–Suzuki-type proximal contraction; an α - θ - generalized Geraghty–Pata–Suzuki-type proximal contraction; and an α - θ - modified Geraghty–Pata–Suzuki-type proximal contraction. These new results generalize, extend, and unify various results from the existing literature. Symmetry plays a crucial role in solving nonlinear problems in operator theory, and the variables involved in the metric space are symmetric. Several illustrative examples are provided to showcase the superiority of our results over existing approaches. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
62. A fast blind image deblurring method using salience map and gradient cepstrum.
- Author
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Liu, Jing, Tan, Jieqing, and He, Lei
- Subjects
NONLINEAR operators ,EXTREME value theory - Abstract
The prior-based blind image deblurring methods have recently achieved good performance. However, many state-of-art algorithms are time-consuming since some nonlinear operators are involved. Presented in this paper is a fast blind image deblurring algorithm which uses the salience map and gradient cepstrum. The inspiration for this work comes from the fact that the extreme values of the salience map of the clear image are more sparse than those of the blurred one. By enforcing the L 0 norm constraint to the terms involving salience map and incorporating them into the traditional deblurring framework, an effective optimization scheme is explored. Furthermore, gradient cepstrum is used to adjust the number of iterations in each scale and determine the size of the initial kernel. Experimental results illustrate that our algorithm outperforms the state-of-art deblurring algorithms in both benchmark datasets and real blur scenes. Besides, this algorithm greatly shortens the running time since it restrains excessive iterations and does not involve any nonlinear operators. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
63. Solvability for a Hadamard-type fractional integral boundary value problem.
- Author
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Jiafa Xu, Jie Liu, and O'Regan, Donal
- Subjects
FUZZY algorithms ,HADAMARD matrices ,FRACTIONAL differential equations ,FIXED point theory ,NONLINEAR operators - Abstract
In this paper, we study an integral boundary value problem involving a Hadamard-type fractional differential equation. Using fixed point theory and upper-lower solutions, we present some sufficient conditions to obtain existence theorems of positive solutions for the problem. Examples are provided to illustrate our results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
64. Discrete time dynamics of a SIRD reinfection model.
- Author
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Eshmatov, F. F., Jamilov, U. U., and Khudoyberdiev, Kh. O.
- Subjects
NONLINEAR operators ,REINFECTION ,DISCRETE-time systems ,NONLINEAR dynamical systems ,DYNAMICAL systems ,STOCHASTIC models - Abstract
This paper deals with a discrete-time dynamical system generated by a modified susceptible–infected–recovered–dead model (SIRD model; nonlinear operator) in three-dimensional simplex. We introduce a novel approach that incorporates the SIRD model with the quadratic stochastic operator (QSO) that allows for real-time forecasting. The basic reproductive number R 0 is obtained. We describe the set of fixed points of the operator and demonstrate that all fixed points are non-hyperbolic. Further, we study the asymptotical behavior of the trajectories of this system and show that SIRD operators have a regularity property. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
65. Coincidence and Common Fixed Point Theorems for Hybrid Mappings.
- Author
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Hamaizia, Taieb
- Subjects
METRIC spaces ,MATHEMATICS ,FIXED point theory ,NONLINEAR operators ,POINT mappings (Mathematics) - Abstract
In this paper, we prove a new coincidence and common fixed point theorem of hybrid mappings using the C-class function and T-weak commutativity. Finally, we give an example to illustrate our result. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
66. Monotonicity results for fractional parabolic equations in the whole space.
- Author
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Luo, Linfeng and Zhang, Zhengce
- Subjects
NONLINEAR operators ,SINGULAR integrals ,AEROSPACE planes ,EQUATIONS ,NONLINEAR equations - Abstract
In this paper, we consider the properties of solutions for the following fractional parabolic equation \begin{document}$ \begin{equation*} \frac{\partial u}{\partial t}(x, t)+(-\Delta)^su(x, t) = f(u(x, t)), \ (x, t)\in\mathbb{R}^N\times\mathbb{R}. \end{equation*} $\end{document} Without assuming any decay behavior of $ u $ near infinity, we first establish a narrow region principle in unbounded domains, then employing the direct method of moving planes, we derive the monotonicity, antisymmetry and non-existence of the solutions. In most previous articles, to carry out the direct method of moving planes in the whole space, they often needed to assume that the solution tends to zero near infinity or that the solution is divided by a function to make the new solution satisfy such an asymptotic decay. Here we develop a new approach–estimating the singular integrals defining $ (-\Delta)^s $ and the derivative of the solution with respect to time along a sequence of approximate extreme points.We believe that the new method employed here will be very helpful to study a class of parabolic equations involving nonlinear nonlocal operators. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
67. Bi-fidelity modeling of uncertain and partially unknown systems using DeepONets.
- Author
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De, Subhayan, Reynolds, Matthew, Hassanaly, Malik, King, Ryan N., and Doostan, Alireza
- Subjects
NONLINEAR operators ,UNCERTAIN systems - Abstract
Recent advances in modeling large-scale, complex physical systems have shifted research focuses towards data-driven techniques. However, generating datasets by simulating complex systems can require significant computational resources. Similarly, acquiring experimental datasets can prove difficult. For these systems, often computationally inexpensive, but in general inaccurate models, known as the low-fidelity models, are available. In this paper, we propose a bi-fidelity modeling approach for complex physical systems, where we model the discrepancy between the true system's response and a low-fidelity response in the presence of a small training dataset from the true system's response using a deep operator network, a neural network architecture suitable for approximating nonlinear operators. We apply the approach to systems that have parametric uncertainty and are partially unknown. Three numerical examples are used to show the efficacy of the proposed approach to model uncertain and partially unknown physical systems. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
68. Probabilistic Measurement, a New Tool to Computing the Spectral-base Equilibrium Points.
- Author
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Jaberi, A. and Goudarzi, H. R.
- Subjects
NONLINEAR operators ,EVOLUTION equations ,EQUILIBRIUM ,HILBERT space ,SCHRODINGER equation - Abstract
In a quantum system, equilibrium points are usually defined by the equation of evolution. The analysis of this process is often done by Schrödinger equation, and by linear operators on a Hilbert space. Regardless of the fact that calculations are based on static-point metrics, due to the chaotic behavior, the realization of practical conditions on space and mappings will be relatively difficult. In addition, access to constructive arguments will enable us to provide a computational method. In this paper, at first we define a probabilistic measurement and combine it with probabilistic domains to obtain a probabilistic model suitable for quantum systems. By extending the mappings to nonlinear operators, we examine the conditions under which stable equilibrium points can be reached. In the application section, using the evolution equation, we will determine the stationary points based on their spectral properties. Also there will be possible to generalize this method to simultaneous measurements. [ABSTRACT FROM AUTHOR]
- Published
- 2023
69. Some Approximation Theorems for a General Class of Discrete Type Operators in Spaces with a Polynomial Weight.
- Author
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Magnucka-Blandzi, Ewa and Walczak, Zbigniew
- Subjects
APPROXIMATION theory ,LINEAR operators ,NONLINEAR operators ,POLYNOMIAL approximation ,MATHEMATICS theorems - Abstract
The paper is devoted approximation of real-valued functions defined on an unbounded interval by linear and non-linear operators. The publication pays special attention to defining class of operators and examining their certain approximation properties. The form of the class of operators given in the present paper makes the achieved results more helpful from the computational point of view. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
70. Superslow relaxation in identical phase oscillators with random and frustrated interactions.
- Author
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Daido, H.
- Subjects
DYNAMICS ,GAUSSIAN distribution ,FIXED point theory ,NONLINEAR operators ,DISTRIBUTION (Probability theory) - Abstract
This paper is concerned with the relaxation dynamics of a large population of identical phase oscillators, each of which interacts with all the others through random couplings whose parameters obey the same Gaussian distribution with the average equal to zero and are mutually independent. The results obtained by numerical simulation suggest that for the infinite-size system, the absolute value of Kuramoto's order parameter exhibits
superslow relaxation , i.e., 1/lnt as timet increases. Moreover, the statistics on both the transient timeT for the system to reach a fixed point and the absolute value of Kuramoto's order parameter att =T are also presented together with their distribution densities over many realizations of the coupling parameters. [ABSTRACT FROM AUTHOR]- Published
- 2018
- Full Text
- View/download PDF
71. Two more approaches for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics.
- Author
-
Liu, Jian
- Subjects
QUANTUM theory ,PHASE space ,EQUILIBRIUM ,HAMILTONIAN systems ,EQUATIONS of motion ,HIGH temperatures ,NONLINEAR operators ,LINEAR operators - Abstract
We show two more approaches for generating trajectory-based dynamics in the phase space formulation of quantum mechanics: 'equilibrium continuity dynamics' (ECD) in the spirit of the phase space continuity equation in classical mechanics, and 'equilibrium Hamiltonian dynamics' (EHD) in the spirit of the Hamilton equations of motion in classical mechanics. Both ECD and EHD can recover exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Both ECD and EHD conserve the quasi-probability within the infinitesimal volume dxtdpt around the phase point (xt, pt) along the trajectory. Numerical tests of both approaches in the Wigner phase space have been made for two strongly anharmonic model problems and a double well system, for each potential auto-correlation functions of both linear and nonlinear operators have been calculated. The results suggest EHD and ECD are two additional potential useful approaches for describing quantum effects for complex systems in condense phase. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
72. An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. II. Thermal correlation functions.
- Author
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Liu, Jian and Miller, William H.
- Subjects
PHASE space ,QUANTUM theory ,QUANTUM trajectories ,NONLINEAR operators ,AUTOCORRELATION (Statistics) ,LINEAR operators ,HARMONIC oscillators - Abstract
We show the exact expression of the quantum mechanical time correlation function in the phase space formulation of quantum mechanics. The trajectory-based dynamics that conserves the quantum canonical distribution-equilibrium Liouville dynamics (ELD) proposed in Paper I is then used to approximately evaluate the exact expression. It gives exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Various methods have been presented for the implementation of ELD. Numerical tests of the ELD approach in the Wigner or Husimi phase space have been made for a harmonic oscillator and two strongly anharmonic model problems, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. It suggests ELD can be a potentially useful approach for describing quantum effects for complex systems in condense phase. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
73. A Convergence Analysis of the Iterated Lavrentiev Regularization Method under a Lipschitz Condition.
- Author
-
Mahale, Pallavi and Singh, Ankit
- Subjects
NONLINEAR operators ,OPERATOR equations ,HILBERT space ,MONOTONE operators - Abstract
Mahale and Nair (2009) considered a iterated Lavrentive regularization method for obtaining stable approximate solution of nonlinear ill-posed operator equation F(x) = y, where F : D (F) ⊂ X → X is a nonlinear monotone operator on Hilbert space X. In this paper, we do convergence analysis of the method under the weaker non-linearity condition than the one considered by Mahale and Nair. We obtain convergence and rate of convergence results for the method merely under Lipschitz's condition. At the end of the paper, we give a numerical example to demonstrate our algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
74. A force function formula for solutions of nonlinear weakly singular Volterra integral equations (WSVIE).
- Author
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Sarfo, Kwasi Frempong, Denteh, William Obeng, Takyi, Ishmael, and Darkwah, Kwaku Forkuoh
- Subjects
- *
VOLTERRA equations , *SINGULAR integrals , *POWER series , *INTEGRAL equations , *NONLINEAR operators - Abstract
In this paper, we examine the nonlinear Weakly Singular Volterra Integral Equation (WSVIE), u(x) = f(x)+∫0x t μ-1/xµ [u(t)]βdt. Al-Jawary and Shehan used the Daftardar-Jafari Method (DJM) and solved the above integral equation for the investigation parameter µ > 1 using specific force functions with µ and β values and obtained unique solutions. We have discovered a force function f(x) = x k1-x γk1/γk1+µ that allows the introduction of noise terms phenomena discovered by Wazwaz that cancel out the terms of the power series in the successive solution terms um, m = 0, 1, 2, ..., n: we thus obtain a maximum finite power series terms for each solution term called truncation point and denoted by x g(n) . Such that the integral solution can be written as u(x) = u0+∑ m n=1 um, where n is finite. Simplifying the solution terms, we get the unique solution u(x) = x k1, irrespective of the n−value in the truncation point. We have discovered a formula relation between the last solution term un and the truncation point as un = anx g(n) . Our results confirm the results of the two solution examples of AL-Jawary and Shehan for the investigation parameter µ > 1. We extend the parameter range to include µ > 1 and 0 < µ ≤ 1 for our solution. In addition, for any chosen rational parameter k1, the solution u(x) = x k1 is extrapolated to be valid for all integer parameter values β ≥ 2 and positive rational parameter values µ > 0 and for any finite value of n ≥ 2. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
75. A density result for doubly nonlinear operators in $ L^1 $.
- Author
-
Collier, Timothy Allen and Hauer, Daniel
- Subjects
NONLINEAR operators ,DENSITY ,POROUS materials - Abstract
The aim of this paper is to provide sufficient conditions implying that the effective domain $ D(A\phi) $ of an $ m $-accretive operator $ A\phi $ in $ L^1 $ is dense in $ L^1 $. Here, $ A\phi $ refers to the composition $ A\circ \phi $ in $ L^1 $ of the part $ A = (\partial\mathcal{E})_{\vert L^{1\cap \infty}} $ in $ L^{1\cap\infty} $ of the subgradient $ \partial\mathcal{E} $ in $ L^2 $ of a convex, proper, lower semicontinuous functional $ \mathcal{E} $ on $ L^2 $ and a continuous, strictly increasing function $ \phi $ on the real line $ \mathbb{R} $. To illustrate the role of the sufficient conditions, we apply our main result to the class of doubly nonlinear operators $ A\phi $, where $ A $ is a classical Leray-Lions operator. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
76. Sharp estimates for the first Robin eigenvalue of nonlinear elliptic operators.
- Author
-
Della Pietra, Francesco and Piscitelli, Gianpaolo
- Subjects
- *
ELLIPTIC operators , *NONLINEAR operators , *EIGENVALUES , *CONVEX domains , *NONLINEAR equations , *ELLIPTIC equations - Abstract
The aim of this paper is to obtain optimal estimates for the first Robin eigenvalue of the anisotropic p -Laplace operator, namely: λ 1 (β , Ω) = min ψ ∈ W 1 , p (Ω) ∖ { 0 } ∫ Ω F (∇ ψ) p d x + β ∫ ∂ Ω | ψ | p F (ν Ω) d H N − 1 ∫ Ω | ψ | p d x , where p ∈ ] 1 , + ∞ [ , Ω is a bounded, anisotropic mean convex domain in R N , ν Ω is its Euclidean outward normal, β is a real number, and F is a sufficiently smooth norm on R N. The estimates we found are in terms of the first eigenvalue of a one-dimensional nonlinear problem, which depends on β and on geometrical quantities associated to Ω. More precisely, we prove a lower bound of λ 1 in the case β > 0 , and a upper bound in the case β < 0. As a consequence, we prove, for β > 0 , a lower bound for λ 1 (β , Ω) in terms of the anisotropic inradius of Ω and, for β < 0 , an upper bound of λ 1 (β , Ω) in terms of β. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
77. Symmetry of Positive Solutions for Fully Nonlinear Nonlocal Systems.
- Author
-
Luo, Linfeng and Zhang, Zhengce
- Subjects
- *
NONLINEAR systems , *NONLINEAR operators , *SYMMETRY - Abstract
In this paper, we consider the nonlinear systems involving fully nonlinear nonlocal operators { F α (u (x)) = v p (x) + k 1 (x) u r (x) , x ∈ ℝ N , G β (v (x)) = u q (x) + k 2 (x) v s (x) , x ∈ ℝ N and { F α (u (x)) = v p (x) | x | a + u r (x) | x | b , x ∈ ℝ N \ { 0 } , G β (v (x)) = u q (x) | x | c + v s (x) | x | d , x ∈ ℝ N \ { 0 } , where ki(x) ≥ 0, i = 1, 2, 0 < α, β < 2, p, q, r, s > 1, a, b, c, d > 0. By proving a narrow region principle and other key ingredients for the above systems and extending the direct method of moving planes for the fractional p-Laplacian, we derive the radial symmetry of positive solutions about the origin. During these processes, we estimate the local lower bound of the solutions by constructing sub-solutions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
78. NEW FIXED POINT RESULTS FOR NONLINEAR FENG-LIU CONTRACTIONS WITH APPLICATIONS.
- Author
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PETRUŞEI, ADRIAN, PETRUŞEI, GABRIELA, and JEN-CHIH YAO
- Subjects
NONLINEAR operators ,NONLINEAR oscillators ,METRIC spaces ,CONTRACTIONS (Topology) - Abstract
In this paper we will extend the concept of multi-valued Feng--Liu contraction, by imposing a nonlinear assumption on the operator. Then, fixed point, strict fixed point and stability theorems for the fixed point inclusion with multi-valued nonlinear Feng--Liu contractions are given. An application illustrates the main theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
79. Approximate controllability of the semilinear population dynamics system with diffusion.
- Author
-
Singh, Ajeet and Shukla, Anurag
- Subjects
POPULATION dynamics ,CONTROLLABILITY in systems engineering ,SYSTEM dynamics ,LAPLACIAN operator ,FUNCTION spaces ,NONLINEAR operators ,LINEAR dynamical systems - Abstract
This paper aims to study the approximate controllability of semilinear population dynamics system with diffusion using semigroup theory. The semilinear population dynamical model with the nonlocal birth process is transformed into a standard abstract semilinear control system by identifying the state, control, and the corresponding function spaces. The state and control spaces are assumed to be Hilbert spaces. The semigroup theory is developed from the properties of the population operators and Laplacian operators. Then the approximate controllability results of the system are obtained using C0$$ {C}_0 $$‐semigroup approach and some other simple conditions on the nonlinear term and operators involved in the model. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
80. Platoon-based collision-free control for connected and automated vehicles at non-signalized intersections.
- Author
-
Gong, Jian, Zhao, Yuan, Cao, Jinde, and Huang, Wei
- Subjects
DIFFERENTIAL equations ,FIXED point theory ,NONLINEAR operators ,MATHEMATICAL singularities ,MATHEMATICAL physics - Abstract
This paper proposes a distributed collision-free control scheme for connected and automated vehicles (CAVs) at a non-signalized intersection. We first divide an intersection area into three sections, i.e., the free zone, the platoon zone, and the control zone. In order to enable the following vehicles to track the trajectory of their leading vehicle in the platoon zone and the control zone, as well as to guarantee the desired distance between any two adjacent vehicles, the distributed platoon controllers are designed. In the control zone, each vehicular platoon is taken as a whole to be coordinated via an intersection coordination unit (ICU). To avoid collision between each pair of the conflicting platoons approaching from different directions, a platoon-based coordination strategy is designed by scheduling the arrival time of each leading vehicle of different platoons. Specially, considering traffic efficiency and fuel economy, the optimal control problem of the leading vehicle is formulated subject to the constraint of allowable minimum arrival time, which is derived from coordination with other approaching platoons. The Pontryagin Minimum Principle (PMP) and phase-plane method are applied to find the optimal control sequences. Numerical simulations show the effectiveness of this scheme. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
81. Symmetry of solutions for asymptotically symmetric nonlocal parabolic equations.
- Author
-
Luo, Linfeng and Zhang, Zhengce
- Subjects
SYMMETRIC functions ,NONLINEAR operators ,EQUATIONS ,SYMMETRY - Abstract
In this paper, we consider the symmetry properties of positive solutions for nonlocal parabolic equations in the whole space. We obtain various asymptotic maximum principles for carrying out the asymptotic method of moving planes. With the help of these results, we show that if the equation converges to a symmetric one, then the solutions will converge to radially symmetric functions. The methods and techniques used here can be easily applied to study a variety of nonlocal parabolic equations with more general operators and nonlinear terms. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
82. Regularity theory for fractional reaction–subdiffusion equation and application to inverse problem.
- Author
-
Van Bang, Tran and Van Tuan, Tran
- Subjects
INVERSE problems ,RESOLVENTS (Mathematics) ,NONLINEAR operators ,EQUATIONS ,PARAMETER identification - Abstract
In this paper, we analyze the regularity in time of solutions for nonlinear fractional reaction–subdiffusion equations (FrRSEs). By constituting regularity estimates of resolvent operator and employing fixed point theorems, we establish some results on the global existence and regularity in time of solutions to FrRSE in two different cases of nonlinear perturbations, namely, sublinear and superlinear cases. As an application of these results, several results on the existence and regularity of solutions in an inverse source problem governed by FrRSE with the additional measurements given at terminal time will be shown. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
83. Iterative manner involving sunny nonexpansive retractions for nonlinear operators from the perspective of convex programming as applicable to differential problems, image restoration and signal recovery.
- Author
-
Damrongsak Yambangwai, Chonjaroen Chairatsiripong, and Tanakit Thianwan
- Subjects
NONEXPANSIVE mappings ,NONLINEAR operators ,CONVEX programming ,DIFFERENTIAL equations ,BANACH spaces - Abstract
In this paper, using sunny nonexpansive retractions which are different from the metric projection in Banach spaces, we develop the CR-iteration algorithm in view of two quasi-nonexpansive nonself mappings and also give the convergence analysis for the proposed method in the setting of uniformly convex Banach spaces. Furthermore, our results can be applied for the purpose of finding common zeros of accretive operators, convexly constrained least square problems and convex minimization problems. Regarding application, some numerical experiments involving real-world problems are provided, with focus on differential problems, image restoration problems and signal recovery problems. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
84. Alternating direction method for the fixed point problem of set-valued mappings with second-order cone double constraints.
- Author
-
Na Mi, Juhe Sun, Li Wang, and Yu Liu
- Subjects
FIXED point theory ,NONLINEAR operators ,EQUILIBRIUM ,STOCHASTIC convergence ,ALGORITHMS - Abstract
This paper focuses on solving a class of equilibrium problems, namely, the fixed point problem of set-valued mappings with second-order cone double constraints. Under certain conditions, the variational inequality form of the fixed point problem of set-valued mappings with second-order cone double constraints is obtained by using the generalized saddle point theory three times. The alternating direction method is used to solve the fixed point problem of set-valued mappings with second-order cone double constraints, and the global convergence of the algorithm is proved. Finally, numerical results of solving five examples with an inexact alternating direction method are given, and the feasibility and effectiveness of the algorithm are demonstrated by comparing with other algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
85. Solving an integral equation via orthogonal generalized α-ψ-Geraghty contractions.
- Author
-
Prakasam, Senthil Kumar, Gnanaprakasam, Arul Joseph, Mani, Gunaseelan, and Jarad, Fahd
- Subjects
INTEGRAL equations ,ORTHOGONAL curves ,BANACH spaces ,FIXED point theory ,NONLINEAR operators - Abstract
In this paper, we introduce orthogonal generalized O-α-ψ-Geraghty contractive type mappings and prove some fixed point theorems in O-complete O-b-metric spaces. We also provide an illustrative example to support our theorem. The results proved here will be utilized to show the existence of a solution to an integral equation as an application. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
86. Some results for multivalued mappings in extended fuzzy b-metric spaces.
- Author
-
Batul, Samina, Mehmood, Faisar, Hussain, Azhar, George, Reny, and Ashraf, Muhammad Sohail
- Subjects
FUZZY algorithms ,INTEGRALS ,DIRICHLET integrals ,FIXED point theory ,NONLINEAR operators - Abstract
In this paper, some fixed point results for multivalued contractions are established in setting G-complete extended fuzzy b-metric spaces. An example is furnished to demonstrate the validity of results. An application of integral type inclusion is given to authenticate the theorems. Our results extend and generalize many existing results in literature. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
87. Inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types.
- Author
-
Luo, Yinglin, Tan, Bing, and Li, Songxiao
- Subjects
BANACH spaces ,ALGORITHMS ,NONLINEAR operators ,NONEXPANSIVE mappings - Abstract
In this paper, inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types are proposed. Weak and strong convergence theorems are established in uniformly convex and q-uniformly smooth Banach spaces. Numerical examples are given to illustrate the effectiveness of our proposed algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
88. Approximating Multiple Roots of Applied Mathematical Problems Using Iterative Techniques.
- Author
-
Behl, Ramandeep, Arora, Himani, Martínez, Eulalia, and Singh, Tajinder
- Subjects
NONLINEAR operators ,NONLINEAR equations ,MULTIPLICITY (Mathematics) ,ITERATIVE methods (Mathematics) - Abstract
In this study, we suggest a new iterative family of iterative methods for approximating the roots with multiplicity in nonlinear equations. We found a lack in the approximation of multiple roots in the case that the nonlinear operator be non-differentiable. So, we present, in this paper, iterative methods that do not use the derivative of the non-linear operator in their iterative expression. With our new iterative technique, we find better numerical results of Planck's radiation, Van Der Waals, Beam designing, and Isothermal continuous stirred tank reactor problems. Divided difference and weight function approaches are adopted for the construction of our schemes. The convergence order is studied thoroughly in the Theorems 1 and 2, for the case when multiplicity p ≥ 2 . The obtained numerical results illustrate the preferable outcomes as compared to the existing ones in terms of absolute residual errors, number of iterations, computational order of convergence (COC), and absolute error difference between two consecutive iterations. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
89. Existence, Data Dependence and Stability of Fixed Points of Multivalued Maps in Incomplete Metric Spaces.
- Author
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Choudhury, Binayak S., Metiya, Nikhilesh, Kundu, Sunirmal, and Khatua, Debashis
- Subjects
FIXED point theory ,METRIC spaces ,BANACH spaces ,NONLINEAR operators ,GRAPHIC methods - Abstract
In this paper we formulate a setvalued fixed point problem by combining four prevalent trends of fixed point theory. We solve the problem by showing that the set of fixed points is nonempty. Further we have a data dependence result pertaining to the problem and also a stability result for the fixed point sets. The main result is extended to metric spaces with a graph. The results are obtained without the use of metric completeness assumption which is replaced by some other conditions suitable for solving the fixed point problem. There are some consequences of the main result. The main result is illustrated with an example. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
90. The initial-nonlinear nonlocal solutions for a parabolic system in a weighted Sobolev space.
- Author
-
Phuong Ngoc, Le Thi and Thanh Long, Nguyen
- Subjects
SOBOLEV spaces ,APPROXIMATION theory ,NONLINEAR operators ,OPTIMISM - Abstract
In this paper, we prove the existence of the initial-nonlinear nonlocal solutions for a parabolic system in a weighted Sobolev space. The methods applied are the Faedo–Galerkin approximation and the general theory of weak compactness in appropriate weighted Sobolev spaces together with using the Poincaré-type operator for dealing nonlinear nonlocal conditions. Furthermore, the boundedness and positivity of solutions depending on the boundedness and positivity of given data are also discussed by using suitable test functions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
91. Quasilinear differential inclusions driven by degenerated p-Laplacian with weight.
- Author
-
Motreanu, Dumitru
- Subjects
DIFFERENTIAL operators ,DIFFERENTIAL inclusions ,NONLINEAR operators ,DIRICHLET problem ,ELLIPTIC equations - Abstract
The main result of the paper provides the existence of a solution to a quasilinear inclusion problem with Dirichlet boundary condition which exhibits a term with full dependence on the solution and its gradient (convection term) and is driven by the degenerated p -Laplacian with weight. The multivalued term in the differential inclusion is in form of the generalized gradient of a locally Lipschitz function expressed through the primitive of a locally essentially bounded function, which makes the problem to be of a hemivariational inequality type. The novelty of our result is that we are able to simultaneously handle three major features: degenerated leading operator, convection term and discontinuous nonlinearity. Results of independent interest regard certain nonlinear operators associated to the differential inclusion. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
92. Preface: Special issue on approximation by linear and nonlinear operators with applications. Part Ⅱ.
- Author
-
Costarelli, Danilo
- Subjects
NONLINEAR operators ,APPROXIMATION theory ,POSITIVE operators ,APPLIED mathematics ,FOURIER analysis ,LINEAR operators - Published
- 2022
- Full Text
- View/download PDF
93. Fixed point theorems of operators with PPF dependence in partial b-metric spaces.
- Author
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Rathee, Savita and Kumari, Neelam
- Subjects
NONLINEAR operators - Abstract
In this paper, "fixed point" theorems of a nonlinear operator are developed, where the domain space is C ([a,b], B) and range space is B, which is a "partial b-metric space" with some conditions. Some results are improved and generalized for "PPF dependent fixed point" in "partial b-metric space". [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
94. Fixed points of anti‐attracting maps and eigenforms on fractals.
- Subjects
FRACTALS ,NONLINEAR operators ,CONVEX sets ,DIRICHLET forms ,FRACTAL analysis - Abstract
An important problem in analysis on fractals is the existence of a self‐similar energy on finitely ramified fractals. The self‐similar energies are constructed in terms of eigenforms, that is, eigenvectors of a special nonlinear operator. Previous results by C. Sabot and V. Metz give conditions for the existence of an eigenform. In this paper, I prove this type of result in a different way. The proof given in this paper is based on a general fixed‐point theorem for anti‐attracting maps on a convex set. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
95. FR-type algorithm for finding approximate solutions to nonlinear monotone operator equations.
- Author
-
Abubakar, Auwal Bala, Muangchoo, Kanikar, Ibrahim, Abdulkarim Hassan, Abubakar, Jamilu, and Rano, Sadiya Ali
- Subjects
OPERATOR equations ,NONLINEAR operators ,ALGORITHMS ,MONOTONE operators ,CONJUGATE gradient methods ,NONLINEAR equations - Abstract
This paper focuses on the problem of convex constraint nonlinear equations involving monotone operators in Euclidean space. A Fletcher and Reeves type derivative-free conjugate gradient method is proposed. The proposed method is designed to ensure the descent property of the search direction at each iteration. Furthermore, the convergence of the proposed method is proved under the assumption that the underlying operator is monotone and Lipschitz continuous. The numerical results show that the method is efficient for the given test problems. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
96. Validity of models for Dreicer generation of runaway electrons in dynamic scenarios.
- Author
-
Olasz, S., Embreus, O., Hoppe, M., Aradi, M., Por, D., Jonsson, T., Yadikin, D., Pokol, G.I., and Team, EU-IM
- Subjects
ELECTRON-electron interactions ,CRITICAL velocity ,NONLINEAR operators ,ELECTRONS ,ELECTRIC fields - Abstract
Runaway electron modelling efforts are motivated by the risk these energetic particles pose to large fusion devices. The sophisticated kinetic models can capture most features of the runaway electron generation but have high computational costs, which can be avoided by using computationally cheaper reduced kinetic codes. This paper compares the reduced kinetic and kinetic models to determine when the former solvers, based on analytical calculations assuming quasi-stationarity, can be used. The Dreicer generation rate is calculated by two different solvers in parallel in a workflow developed in the European integrated modelling framework, and this is complemented by calculations of a third code that is not yet integrated into the framework. Runaway Fluid, a reduced kinetic code, NORSE, a kinetic code using non-linear collision operator, and DREAM, a linearized Fokker–Planck solver, are used to investigate the effect of a dynamic change in the electric field for different plasma scenarios spanning across the whole tokamak-relevant range. We find that on time scales shorter than or comparable to the electron–electron collision time at the critical velocity for runaway electron generation, kinetic effects not captured by reduced kinetic models play an important role. This characteristic time scale is easy to calculate and can reliably be used to determine whether there is a need for kinetic modelling or cheaper reduced kinetic codes are expected to deliver sufficiently accurate results. This criterion can be automated, and thus it can be of great benefit for the comprehensive self-consistent modelling frameworks that are attempting to simulate complex events such as tokamak start-up or disruptions. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
97. New iterative methods for nonlinear operators as concerns convex programming applicable in differential problems, image deblurring, and signal recovering problems.
- Author
-
Chairatsiripong, Chonjaroen, Yambangwai, Damrongsak, and Thianwan, Tanakit
- Subjects
NONLINEAR operators ,CONVEX programming ,NONEXPANSIVE mappings ,METRIC projections ,BANACH spaces ,SIGNALS & signaling - Abstract
In this paper, using sunny nonexpansive retractions, which are different from the metric projection in Banach spaces, a new type of study regarding the iterative methods in view of two quasi‐nonexpansive nonself mappings is presented. We also give the convergence analysis for the proposed method in the background of uniformly convex Banach spaces. Moreover, we apply our results to find solutions of common zeros of accretive operators, convexly constrained least square problems, and convex minimization problems. Furthermore, we also discuss novel applications of these methods to differential problems, image deblurring, and signal recovering problems. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
98. Semilocal Convergence of a Multi-Step Parametric Family of Iterative Methods.
- Author
-
Villalba, Eva G., Martínez, Eulalia, and Triguero-Navarro, Paula
- Subjects
DIFFERENCE operators ,NONLINEAR operators ,ITERATIVE methods (Mathematics) ,FAMILIES - Abstract
In this paper, we deal with a new family of iterative methods for approximating the solution of nonlinear systems for non-differentiable operators. The novelty of this family is that it is a m-step generalization of the Steffensen-type method by updating the divided difference operator in the first two steps but not in the following ones. This procedure allows us to increase both the order of convergence and the efficiency index with respect to that obtained in the family that updates divided differences only in the first step. We perform a semilocal convergence study that allows us to fix the convergence domain and uniqueness for real applied problems, where the existence of a solution is not known a priori. After this study, some numerical tests are developed to apply the semilocal convergence theoretical results obtained. Finally, mediating the dynamic planes generated by the different numerical methods that compose the family, we study the symmetry of the basins of attraction generated by each solution, the shape of these basins, and the convergence to each root of a polynomial function. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
99. Pyramid transform of manifold data via subdivision operators.
- Author
-
Mattar, Wael and Sharon, Nir
- Subjects
PYRAMIDS ,DATA structures ,ELECTRONIC data processing ,NONLINEAR operators ,SUBDIVISION surfaces (Geometry) ,MULTISCALE modeling - Abstract
Multiscale transforms have become a key ingredient in many data processing tasks. With technological development we observe a growing demand for methods to cope with nonlinear data structures such as manifold values. In this paper we propose a multiscale approach for analyzing manifold-valued data using a pyramid transform. The transform uses a unique class of downsampling operators that enable a noninterpolating subdivision schemes as upsampling operators. We describe this construction in detail and present its analytical properties, including stability and coefficient decay. Next, we numerically demonstrate the results and show the application of our method to denoising and anomaly detection. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
100. Liouville-Type Theorem for Nonlinear Elliptic Equations Involving Generalized Greiner Operator.
- Author
-
Shi, Wei
- Subjects
ELLIPTIC equations ,NONLINEAR equations ,NONLINEAR operators - Abstract
In this paper, we study the Liouville-type behaviors of the generalized Greiner operators with nonlinear boundary value conditions. We use the technique based upon the method of moving planes. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
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