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Tautenhahn (2002) studied the Lavrentiev regularization method (LRM) to approximate a stable solution for the ill-posed nonlinear equation κ (u) = v , where κ : D (κ) ⊆ X ⟶ X is a nonlinear monotone operator and X is a Hilbert space. The operator in the example used in Tautenhahn's paper was not a monotone operator. So, the following question arises. Can we use LRM for ill-posed nonlinear equations when the involved operator is not monotone? This paper provides a sufficient condition to employ the Lavrentiev regularization technique to such equations whenever the operator involved is non-monotone. Under certain assumptions, the error analysis and adaptive parameter choice strategy for the method are discussed. Moreover, the developed theory is applied to two well-known ill-posed problems—inverse gravimetry and growth law problems. [ABSTRACT FROM AUTHOR]

In this paper, we study a noncoercive nonlinear elliptic operator with a drift term in an unbounded domain. The singular first-order term grows like | E (x) | | ∇ u | , where E (x) is a vector field belonging to a suitable Morrey-type space. Our operator arises as a stationary equation of diffusion–advection problems. We prove existence, regularity, and uniqueness theorems for a Dirichlet problem. To obtain our main results, we use the weak maximum principle and the same a priori estimates. [ABSTRACT FROM AUTHOR]

This paper is concerned with the study of equations of viscous compressible and heat-conducting full magnetohydrodynamic (MHD) steady flows in a horizontal layer under the gravitational force and a large temperature gradient across the layer. We assume as boundary conditions, periodic conditions in the horizontal directions, while in the vertical directions, slip-boundary is assumed for the velocity, vertical conditions for the magnetic field, and fixed temperature or fixed heat flux are prescribed for the temperature. The existence of stationary solution in a small neighborhood of a stationary profile close to hydrostatic state is obtained in Sobolev spaces as a fixed point of some nonlinear operator. [ABSTRACT FROM AUTHOR]

Collage Theorem provides a bound for the distance between an element of a given space and a fixed point of a self-map on that space, in terms of the distance between the point and its image. We give in this paper some results of Collage type for Reich mutual contractions in b-metric and strong b-metric spaces. We give upper and lower bounds for this distance, in terms of the constants of the inequality involved in the definition of the contractivity. Reich maps contain the classical Banach contractions as particular cases, as well as the maps of Kannan type, and the results obtained are very general. The middle part of the article is devoted to the invertibility of linear operators. In particular we provide criteria for invertibility of operators acting on quasi-normed spaces. Our aim is the extension of the Casazza-Christensen type conditions for the existence of inverse of a linear map defined on a quasi-Banach space, using different procedures. The results involve either a single map or two operators. The latter case provides a link between the properties of both mappings. The last part of the article is devoted to study the construction of fractal curves in Bochner spaces, initiated by the first author in a previous paper. The objective is the definition of fractal curves valued on Banach spaces and Banach algebras. We provide further results on the fractal convolution of operators, defined in the same reference, considering in this case the nonlinear operators. We prove that some properties of the initial maps are inherited by their convolutions, if some conditions on the elements of the associated iterated function system are satisfied. In the last section of the paper we use the invertibility criteria given before in order to obtain perturbed fractal spanning systems for quasi-normed Bochner spaces composed of Banach-valued integrable maps. These results can be applied to Lebesgue spaces of real valued functions as a particular case. [ABSTRACT FROM AUTHOR]

This paper aims to present a hybrid method to solve nonlinear constrained optimization problems and engineering design problems (EDPs). The hybrid method is a combination of monarch butterfly optimization (MBO) with the cross-over and mutation operators of the genetic algorithm (GA). It is called a hybrid monarch butterfly optimization with genetic algorithm operators (MBO-GAO). Combining MBO and GA operators is meant to overcome the drawbacks of both algorithms while merging their advantages. The self-adaptive cross-over and the real-valued mutation are the GA operators that are used in MBO-GAO. These operators are merged in a distinctive way within MBO processes to improve the variety of solutions in the later stages of the search process, speed up the convergence process, keep the search from getting stuck in local optima, and achieve a balance between the tendencies of exploration and exploitation. In addition, the greedy approach is presented in both the migration operator and the butterfly adjusting operator, which can only accept offspring of the monarch butterfly groups who are fitter than their parents. Finally, popular test problems, including a set of 19 benchmark problems, are used to test the proposed hybrid algorithm, MBO-GAO. The findings obtained provide evidence supporting the higher performance of MBO-GAO compared with other search techniques. Additionally, the performance of the MBO-GAO is examined for several EDPs. The computational results show that the MBO-GAO method exhibits competitiveness and superiority over other optimization algorithms employed for the resolution of EDPs. [ABSTRACT FROM AUTHOR]

In this paper, we extend the invariant subspace method to a class of short pulse-type equations. Complete classification results with invariant subspaces from 2 to 5 dimensions are provided. The key step is to take subspaces of solutions of linear ordinary differential equations as invariant subspaces that nonlinear operators admit. Some concrete examples and corresponding reduced systems are presented to illustrate this method. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the existence of positive solutions for a singular tempered sub-diffusion fractional model involving a quasi-homogeneous nonlinear operator. By using the spectrum theory and computing the fixed point index, some new sufficient conditions for the existence of positive solutions are derived. It is worth pointing out that the nonlinearity of the equation contains a tempered fractional sub-diffusion term, and is allowed to possess strong singularities in time and space variables. In particular, the quasi-homogeneous operator is a nonlinear and non-symmetrical operator. [ABSTRACT FROM AUTHOR]

In this paper, we investigated Caputo fractional integro-differential equations with noninstantaneous impulses and nonlocal conditions. By employing the solution operator, the Mönch fixed point theorem, and the stepwise estimation method, we eliminated the Lipschitz condition of the nonlinear term, while also dispensing with the requirement for the compressibility coefficient condition 0 < k < 1. The main results presented represented a generalization and enhancement of previous findings. Furthermore, an example was provided to verify the application of our main results. [ABSTRACT FROM AUTHOR]

The formulation of models and solutions for various physical problems are the primary goals of scientific achievements in engineering and physics. Our paper focuses on using the Caputo fractional derivative operator to solve nonlinear fractional logistic differential equations. In order to solve general nonlinear fractional differential equations, we first introduce a novel numerical methodology termed the Homotopy perturbation transform method. The perturbation approach and the Yang transform method are combined to create the suggested strategy. Second, we introduce a new hybrid method that uses the time-fractional Caputo derivative to approximate and analytically solve nonlinear fractional logistic differential equations. This method combines the Yang transform with the decomposition method. To validate the analysis, we offer three numerical cases of nonlinear fractional logistic differential equations employing the Caputo fractional derivative operator. The resulting solutions exhibit rapid convergence and are presented in series form. In order to verify the efficacy and relevance of the suggested methodologies, the investigated issues were assessed through the implementation of different fractional orders. We examine and show that, under the specified initial conditions, the solution approaches under evaluation are accurate and effective. Graphs in two and three dimensions show the results that were obtained. Numerical simulations are presented to confirm the efficacy of the strategies. The numerical results show that an accurate, reliable, and efficient approximation can be obtained with a minimal number of terms. The results obtained demonstrate that the new analytical solution method is easy to apply and very successful in solving difficult fractional problems that occur in relevant engineering and scientific domains. [ABSTRACT FROM AUTHOR]

In this paper, the existence of the solutions of a class of weakly singular integral equations in Banach algebra is investigated. The basic tool used in investigations is the technique of the measure of non-compactness and Petryshyn's fixed point theorem. Also, for the applicability of the obtained results, some examples are given. [ABSTRACT FROM AUTHOR]

In this paper, by providing an example, I show that the condition which produced by Radenović and Kadelburg in [Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl. 60 (2010) pp. 1776-1783] is not sufficient for uniqueness of the fixed point. Furthermore, a new sufficient condition is introduced for the uniqueness of the fixed point. Some suitable examples are furnished to demonstrate the validity of the hypotheses of my results. [ABSTRACT FROM AUTHOR]

In the present paper, a nonlinear system of sine-Gordon equations that describes the DNA dynamics is considered. A novel unconditionally stable second-order accuracy difference scheme corresponding to the system of sine-Gordon equations is presented. In this work, for the first time in the literature, weak solution of this difference scheme is studied. The existence and uniqueness of the weak solution for the difference scheme are proved in the space of distributions, and the methods of variational calculus are applied. The finite-difference method and the fixed point theory are used in combination to perform numerical experiments that verify the theoretical statements. [ABSTRACT FROM AUTHOR]

In the context of observers, any mathematical model accord- ing to the viewpoint of an observer Θ is called a relative model. The purpose of the present paper is to study the relative model of logical en- tropy. Given an observer Θ, we define the relative logical entropy and relative conditional logical entropy of a sub-σΘ-algebra having finitely many atoms on the relative probability Θ−measure space and prove the ergodic properties of these measures. Finally, it is shown that the relative logical entropy is invariant under the relation of equivalence modulo zero. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to prove the existence and uniqueness of mild solution for abstract differential equations by using the resolvent operators and fixed point theorem. Moreover, we studied some examples on partial differential equation with Caputo-Fabrizio derivative. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new software framework for the offline calculation of tracer transport in the ocean. The Fast Equilibration of Ocean Tracers Software (FEOTS) is an end-to-end set of tools to efficiently calculate tracer distributions on a global or regional sub-domain using transport operators diagnosed from a comprehensive ocean model. To the best of our knowledge, this is the first application of a transport matrix model to an eddying ocean state. While a Newton–Krylov-based equilibration capability is still under development and not presented here, we demonstrate in this paper the transient modeling capabilities of FEOTS in an application focused on the Argentine Basin, where intense eddy activity and the Zapiola Anticyclone lead to strong mixing of water masses. The demonstration illustrates progress in developing offline passive tracer simulation capabilities, while highlighting the challenges of the impulse response functions approach in capturing tracer transports by a non-linear advection scheme. Our future work will focus on improving the computational efficiency of the code to reduce time-to-solution, using different basis functions to better represent non-linear advection operators, applying FEOTS to a parent model with unstructured grids (Ocean Model for Prediction Across Scales, MPAS-Ocean), and fully implementing a Newton–Krylov steady-state solver. [ABSTRACT FROM AUTHOR]

It is well known that sublinear operators and superlinear operators are two classes of important nonlinear operators in nonlinear analysis and dynamical systems. Since sublinear operators have only weak nonlinearity, this advantage makes it easy to deal with them. However, superlinear operators have strong nonlinearity, and there are only a few results about them. In this paper, the convergence of Picard iteration for the superlinear operator A is obtained based on the conditions that the fixed point equation Ax = x has a strong upper solution and a lower solution (or alternatively, an upper solution and a strong lower solution). Besides, the uniqueness of the fixed point of strongly increasing operators as well as the global attractivity of strongly monotone dynamical systems are also discussed. In addition, the main results are applied to monotone dynamics of superlinear operators and nonlinear integral equations. The method used in our work develops the traditional method of upper and lower solutions. Since a strong upper (upper) solution and a lower (strong lower) solution are easily checked, the obtained results are effective and practicable in the study of nonlinear equations and dynamical systems. The main novelty is that this paper provides new fixed point results for increasing superlinear operators and the obtained results are applied to strongly monotone systems to investigate their global attractivity. [ABSTRACT FROM AUTHOR]

This paper presents a novel concept of G -Hardy-Rogers functional operators on metric spaces endowed with a graph. It investigates sufficient circumstances under which such a mapping becomes a Picard operator. As applications of the principal idea discussed herein, a few important corresponding fixed point results in ordered metric spaces and cyclic operators are pointed out and analyzed. For upcoming research papers in this field, comparative graphical illustrations are created to highlight the pre-eminence of proposed notions with respect to the existing ones. [ABSTRACT FROM AUTHOR]

Purpose: Entrepreneurship as a development engine has a distinct character in the economic growth of countries. Therefore, governments must support entrepreneurship in order to succeed in the future. The best way to improve the performance of this entrepreneurial advocacy is through efficient measurement methods. For this reason, the purpose of this paper is to propose a new integrated dynamic multi-attribute decision-making (MADM) model based on neutrosophic set (NS) for assessment of the government entrepreneurship support. Design/methodology/approach: Due to the nature of entrepreneurship issues, which are multifaceted and full of uncertain, indeterminate and ambiguous dimensions, this measurement requires multi-criteria decision-making methods in spaces of uncertainty and indeterminacy. Also, due to the change in the size of indicators in different periods, researchers need a special type of decision model that can handle the dynamics of indicators. So, in this paper, the authors proposed a dynamic neutrosophic weighted geometric operator to aggregate dynamic neutrosophic information. Furthermore, in view of the deficiencies of current dynamic neutrosophic MADM methods a compromised model based on time degrees was proposed. The principle of time degrees was introduced, and the subjective and objective weighting methods were synthesized based on the proposed aggregated operator and a nonlinear programming problem based on the entropy concept was applied to determine the attribute weights under different time sequence. Findings: The information of ten countries with the indicators such as connections (C), the country's level of education and experience (EE), cultural aspects (CA), government policies (GP) and funding (F) over four years was gathered and the proposed dynamic MADM model to assess the level of entrepreneurial support for these countries. The findings show that the flexibility of the model based on decision-making thought and we can see that the weights of the criteria have a considerable impact on the final evaluations. Originality/value: In many decision areas the original decision information is usually collected at different periods. Thus, it is necessary to develop some approaches to deal with these issues. In the government entrepreneurship support problem, the researchers need tools to handle the dynamics of indicators in neutrosophic environments. Given that this issue is very important, nonetheless as far as is known, few studies have been done in this area. Furthermore, in view of the deficiencies of current dynamic neutrosophic MADM making methods a compromised model based on time degrees was proposed. Moreover, the presented neutrosophic aggregation operator is very suitable for aggregating the neutrosophic information collected at different periods. The developed approach can solve the several problems where all pieces of decision information take the form of neutrosophic information collected at different periods. [ABSTRACT FROM AUTHOR]

In this paper, we study the tangential touch and C¹ regularity of the free boundary near the fixed boundary of the double obstacle problem for Laplacian and fully nonlinear operator. The main idea to have the properties is regarding the upper obstacle as a solution of the single obstacle problem. Then, in the classification of global solutions of the double problem, it is enough to consider only two cases for the upper obstacle, a/2 xn² or a/2 xn² + bxnx1 for some b ∈ ℝ, b ≠ 0. The second one is a new type of upper obstacle, which does not exist in the study of local regularity of the free boundary of the double problem. Thus, in this paper, a new type of difficulties that come from the second type upper obstacle is mainly studied. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which is determined by assigning operators and operands to the nodes. Cozad and Sahinidis propose a nonconvex mixed-integer nonlinear program (MINLP), in which binary variables are used to assign operators and nonlinear expressions are used to propagate data values through nonlinear operators, such as square, square root, and exponential. We extend this formulation by adding new cuts that improve the solution of this challenging MINLP. We also propose a heuristic that iteratively builds an expression tree by solving a restricted MINLP. We perform computational experiments and compare our approach with a mixed-integer program–based method and a neural network–based method from the literature. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the Applied Mathematics activity within the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research [Grant DE-AC02-06CH11357]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0050) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0050). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the optimal risk-sensitive reward for Markov decision processes with compact state space and action space converges to the optimal average reward as the risk-sensitive factor tends to 0. In doing so, a variational formula for the optimal risk-sensitive reward is derived. An extension of the Kreĭn-Rutman Theorem to certain nonlinear operators is involved. Based on these, partially observable Markov decision processes are also investigated. A portfolio optimization problem is presented as an example of an application of the approach, in which a duality-relation between the maximization of risk-sensitive reward and the maximization of upside chance for out-performance over the optimal average reward is established. [ABSTRACT FROM AUTHOR]

In this paper, we study a new filtration class MF α , β μ , associated with the filtration of infinitesimal generators, by using the nonlinear fractional differential operator and study certain properties, like sharp Fekete–Szegö inequalities and filtration problems. [ABSTRACT FROM AUTHOR]

In this paper, we prove the following generalization of the classical Darbo fixed point principle : Let X be a Banach space and µ be a montone measure of noncompactness on X which satisfies the generalized Cantor intersection property. Let C be a nonempty bounded closed convex subset of X and T : C → C be a continuous mapping such that for any countable set Ω ⊂ C, we have µ(T(Ω)) ≤ kµ(Ω), where k is a constant, 0 ≤ k < 1. Then T has at least one fixed point in C. The proof is based on a combined use of topological methods and partial ordering techniques and relies on the Schauder and the Knaster-Tarski fixed point principles. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove a common fixed point theorem for a pair of mappings satisfying an implicit relation, generalizing the main results from [6], [10], [11], [13] and other papers. [ABSTRACT FROM AUTHOR]

In this paper, a novel parabolic system involving nonlinear and nonhomogeneous partial differential operator with variable growth structure is introduced for investigating the image denoising and restoration. More precisely, our model is based on regularizing the classical models involving variable exponent operators by considering a nonlinear operator with double phase flux. We begin by investigating theoretically the solvability to the parabolic system under consideration. Under the setting of Musielak-Orlicz spaces, we build a suitable functional framework to study the proposed system. Therefore, we develop the Faedo-Galerkin approach to demonstrate the existence and uniqueness of a weak solution to our model. To illustrate our theoretical results in the context of image noise removal, we present various numerical implementations on some grayscale images. To enrich these simulations, we test the robustness efficiency of the proposed model in the so-called Magnetic Resonance Images (MRI). The obtained numerical results claim that our model is more efficient and robust against noise, in comparison (visually and quantitatively) to some existing state-of-the-art methods. • A novel nonlinear parabolic system is introduced. • The theoretical results are applied to the image denoising and restoration. • Various numerical implementations on some grayscale images are carried out. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

Let X be a linear space over K ∈ { R , C } , Y be a real or complex Banach space and f : X n → Y . With some fixed a j i , C i 1 ... i n ∈ K ( j ∈ { 1 , ... , n } , i , i k ∈ { 1 , 2 } , k ∈ { 1 , ... , n } ), we study, using the direct and the fixed point methods, the stability and the general stability of the equation f (a 11 x 11 + a 12 x 12 , ... , a n 1 x n 1 + a n 2 x n 2) = ∑ 1 ≤ i 1 , ... , i n ≤ 2 C i 1 ... i n f (x 1 i 1 , ... , x n i n ) , for all x j i j ∈ X ( j ∈ { 1 , ... , n } , i j ∈ { 1 , 2 } ). Our paper generalizes several known results, among others concerning equations with symmetric coefficients, such as the multi-Cauchy equation or the multi-Jensen equation as well as the multi-Cauchy–Jensen equation. We also prove the hyperstability of the above equation in m-normed spaces with m ≥ 2 . [ABSTRACT FROM AUTHOR]

In this paper, we propose and justify a spline-collocation method with first-order splines for approximate solution of nonlinear hypersingular integral equations of Prandtl's type. We obtained the estimates of the convergence rate and the method error. The constructed computational scheme includes a continuous method for solving nonlinear operator equations, which is stable for perturbations of the coefficients and the right-hand sides of equations. [ABSTRACT FROM AUTHOR]

The present manuscript examines different forms of Initial-Value Problems (IVPs) featuring various types of Ordinary Differential Equations (ODEs) by proposing a proficient modification to the famous standard Adomian decomposition method (ADM). The present paper collected different forms of inverse integral operators and further successfully demonstrated their applicability on dissimilar nonlinear singular and nonsingular ODEs. Furthermore, we surveyed most cases in this very new method, and it was found to have a fast convergence rate and, on the other hand, have high precision whenever exact analytical solutions are reachable. [ABSTRACT FROM AUTHOR]

Kolmogorov-Petrovskii-Piskunov equation can be regarded as a generalized form of the Fitzhugh-Nagumo, Fisher and Huxley equations which have many applications in physics, chemistry and biology. In this paper, two fractional extended versions of the non-linear Kolmogorov-Petrovskii-Piskunov equation are solved by analytical methods. Firstly, a new and more general fractional derivative is defined and some properties of it are given. Secondly, a solution in the form of operator representation of the non-linear Kolmogorov-Petrovskii- Piskunov equation with the defined fractional derivative is obtained. Finally, some exact solutions including kink-soliton solution and other solutions of the non-linear Kolmogorov-Petrovskii-Piskunov equation with Khalil et al.'s fractional derivative and variable coefficients are obtained. It is shown that the fractional- order affects the propagation velocity of the obtained kink-soliton solution. [ABSTRACT FROM AUTHOR]