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We examine a free transmission problem driven by fully nonlinear elliptic operators. Since the transmission interface is determined endogenously, our analysis regards this object as a free boundary. We start by relating our problem with a pair of viscosity inequalities. Then, approximation methods ensure that strong solutions are of class C 1;Log-Lip, locally. In addition, under further conditions on the problem, we prove quadratic growth of the solutions away from branch points. [ABSTRACT FROM AUTHOR]

The aim of the paper is to discuss data dependence, existence of fixed points, strict fixed points, and well posedness of some multivalued generalized contractions in the setting of complete metric spaces. Using auxiliary functions, we introduce Wardowski type multivalued nonlinear operators that satisfy a novel class of contractive requirements. Furthermore, the existence and data dependence findings for these multivalued operators are obtained. A nontrivial example is also provided to support the results. The results generalize, improve, and extend existing results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the optimal dividend problem in a discrete-time risk model with interest is discussed. Assume that the premium received per unit time is a positive real-valued random variable, and the sequence of premiums is a Markov chain owing to the environmental effects. In arbitrary unit time whether a claim occurs or not is related to the premium received in the corresponding period. Under the constraint of a given survival probability, the optimal control strategy for dividends paid periodically to the shareholders is considered. We provide some properties and an algorithm for the optimal control strategy by structuring a non-linear operator and applying the fixed point theorem. Numerical examples are presented to illustrate the algorithm. [ABSTRACT FROM AUTHOR]

The purpose if this paper is to present a fixed point result constructed by finite sequences. Using iterated function systems and related fractal operators, a mixed patterns generated by the a finite sequence patterns construct the sets of patterns built by black and white squares. A complete metric space related to a mixed pattern sequence is defined using the distance based on difference of the black squares' area. The main result of the paper highlights that these fractal operators has unique fixed points for the sets generated by the mixed patterns. Moreover, the main theorem is also applied for Vicsek fractals such that results also hold for mixed Vicsek patterns. Motivated by various studies on growing graph sequences and related large structures, this paper underlines a new connection between fixed point theory and network science. Using circle patterns, the paper also interprets the main result on sets mixed patterns based on touching circles. Thus, the paper focuses a fixed point theorem on the sets mixed patterns built by iterated function systems and the distances calculated between the areas of these geometric shapes. [ABSTRACT FROM AUTHOR]

This paper considers a class of neutral impulsive stochastic integro-differential inclusion with nonlocal conditions involving the Caputo fractional derivative of order 1 < α< 2 in a Hilbert space. A new set of sufficient conditions for the approximate controllability of semilinear fractional stochastic systems is derived utilizing solution operator, stochastic analysis, fractional calculus and fixed point theorem for a multivalued operator under the assumption that the corresponding linear system is approximately controllable. An example is provided to illustrate the derived theory at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a system of variational inclusions called system of nonlinear variational inclusion problem involving A-monotone mappings in real Hilbert spaces. By means of resolvent operator technique, we suggest an resolvent iterative algorithm for finding the approximate solution of this system and discuss the convergence criteria of the sequences generated by the resolvent iterative algorithm under some suitable conditions. [ABSTRACT FROM AUTHOR]

Neural networks have revolutionized the field of data science, yielding remarkable solutions in a data-driven manner. For instance, in the field of mathematical imaging, they have surpassed traditional methods based on convex regularization. However, a fundamental theory supporting the practical applications is still in the early stages of development. We take a fresh look at neural networks and examine them via nonlinear eigenvalue analysis. The field of nonlinear spectral theory is still emerging, providing insights about nonlinear operators and systems. In this paper we view a neural network as a complex nonlinear operator and attempt to find its nonlinear eigenvectors. We first discuss the existence of such eigenvectors and analyze the kernel of ReLU networks. Then we study a nonlinear power method for generic nonlinear operators. For proximal operators associated to absolutely one-homogeneous convex regularization functionals, we can prove convergence of the method to an eigenvector of the proximal operator. This motivates us to apply a nonlinear method to networks which are trained to act similarly as a proximal operator. In order to take the nonhomogeneity of neural networks into account we define a modified version of the power method. We perform extensive experiments for different proximal operators and on various shallow and deep neural networks designed for image denoising. Proximal eigenvectors will be used for geometric analysis of graphs, as clustering or the computation of distance functions. For simple neural nets, we observe the influence of training data on the eigenvectors. For state-of-the-art denoising networks, we show that eigenvectors can be interpreted as (un)stable modes of the network, when contaminated with noise or other degradations. [ABSTRACT FROM AUTHOR]

In this paper, we consider a new resolvent operator associated with XORNODSM mappings and give some of its fascinating properties supported by a well constructed example. As an application, we introduce and study a system of general mixed variational inclusions involving ⊕ operation in ordered Hilbert spaces. Further, we propose a perturbed Mann Iterative Algorithm with errors for approximating the solution of this class of problems. Our results can be complemented as the refinement and generalization of the corresponding results of recent works. [ABSTRACT FROM AUTHOR]

Fractional calculus has been very popular due to the application in real world problems. This paper aimed to investigate the existence, uniqueness and Ulam stability for nonlinear fractional pantograph differential equations with generalized nonlocal boundary conditions involving Hilfer fractional derivative. The analysis were done through Banach and Kranoselskii's fixed point theorems. Finally, example are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

The goals of the present paper are to introduce truncated Lupaş type operators of max-product kind and give an estimation for the degree of approximation with respect to first modulus of continuity function. We prove that this estimate can not be improved; on the other hand, for some subclasses of functions, better degree of approximation is obtained. We also showed the piecewise convexity of the constructed operators on the interval [0, 1]. [ABSTRACT FROM AUTHOR]

The ubiquity of semilinear parabolic equations is clear from their numerous applications ranging from physics and biology to materials and social sciences. In this paper, we consider a practically desirable property for a class of semilinear parabolic equations of the abstract form ut = u + f[u], with a linear dissipative operator and f a nonlinear operator in space, namely, a time-invariant maximum bound principle, in the sense that the timedependent solution u preserves for all time a uniform pointwise bound in absolute value imposed by its initial and boundary conditions. We first study an analytical framework for sufficient conditions on and f that lead to such a maximum bound principle for the time-continuous dynamic system of infinite or finite dimensions. Then we utilize a suitable exponential time-differencing approach with a properly chosen generator of the contraction semigroup to develop first- and second-order accurate temporal discretization schemes that satisfy the maximum bound principle unconditionally in the time-discrete setting. Error estimates of the proposed schemes are derived along with their energy stability. Extensions to vector- and matrix-valued systems are also discussed. We demonstrate that the abstract framework and analysis techniques developed here offer an effective and unified approach to studying the maximum bound principle of the abstract evolution equation that covers a wide variety of well-known models and their numerical discretization schemes. Some numerical experiments are also carried out to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the following generalized fully nonlinear nonlocal operators: Fs,m(u(x)) = cN,smN/2+sP.V. ∫RNG(u(x)−u(y))/|x−y|N/2+s KN/2+s(m|x−y|)dy+m2su(x), where s ∈ (0,1) and mass m > 0. By establishing various maximal principle and using the direct method of moving plane, we prove the monotonicity, symmetry and uniqueness for solutions to fully nonlinear nonlocal equation in unit ball, RN, RN+ and a coercive epigraph domain Ω in RN respectively. [ABSTRACT FROM AUTHOR]

This paper proposes a resonant electric cradle design with infant cries recognition, employing an Arduino UNO as the core processor. For most commercially available electric cradles, the drive motor is closely combined with the bearing on the top, resulting in a lot of energy consumption. In this proposal, a ball bearing design was adopted and the driving force is under the cradle to increase the distance from the object to fulcrum and torque. The sensors are designed to detect the oscillation state, and then the force is driven at the critical time to achieve the maximum output response while saving energy according to the principle of resonance. As for the driving forces, the winding power and motors are carefully placed under the cradle. The sensors, including the three-axis accelerometer and infrared sensor, are tested and applied under swinging amplitude control. In addition, infant cry recognition technology was incorporated in the design to further develop its functionality, which is a rare feature in this kind of hardware. The proposed nonlinear operator of fundamental frequency (f0) analysis is able to identify different types of infant cries. In conclusion, this paper proposes an energy-saving electric cradle with infant cries recognition and the experimental results demonstrate the effectiveness of this approach. [ABSTRACT FROM AUTHOR]

In this paper, impulsive Lasota-Wazewska model with infinite delay is studied. By using fixed point theorem of decreasing operator, we obtain sufficient conditions for the existence of unique almost periodic positive solution. Particularly, we give iterative sequence, which converges to the almost periodic positive solution. Moreover, we investigate exponential stability of the almost periodic positive solution by Liapunov functional. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we, consider an n‐th order nonlinear difference equation with parameter dependence. An exhaustive study of the related Green's function is done. The exact expression of the function is given. The range of parameter for which either it has constant sign or it changes sign is obtained. Some existence results for the nonlinear problem are deduced by using the classical Krasnosel'skii's fixed point theorem on cones and fixed point index theory. [ABSTRACT FROM AUTHOR]

In this paper, we consider a generalized predator‐prey system with prey‐taxis under the Neumann boundary condition. We investigate the local and global asymptotical stability of constant steady states (including trivial, semitrivial, and interior constant steady states). On the basis of a priori estimate and the fixed‐point index theory, several sufficient conditions for the nonexistence/existence of nonconstant positive solutions are given. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with a problem of an equitable allocation. We consider the concept of ψ‐equity, which is a general concept of equity. We provide a series of examples of equity concepts that are captured by ψ‐equity. We show the existence of an efficient and ψ‐equitable allocation by employing Kakutani's fixed‐point theorem. [ABSTRACT FROM AUTHOR]

The maximum bound principle (MBP) is an important property for a large class of semilinear parabolic equations, in the sense that the time-dependent solution of the equation with appropriate initial and boundary conditions and nonlinear operator preserves for all time a uniform pointwise bound in absolute value. It has been a challenging problem to design unconditionally MBPpreserving high-order accurate time-stepping schemes for these equations. In this paper, we combine the integrating factor Runge--Kutta (IFRK) method with the linear stabilization technique to develop a stabilized IFRK (sIFRK) method, and we successfully derive sufficient conditions for the proposed method to preserve the MBP unconditionally in the discrete setting. We then elaborate some sIFRK schemes with up to the third-order accuracy, which are proven to be unconditionally MBP-preserving by verifying these conditions. In addition, it is shown that many classic strong stability-preserving sIFRK schemes do not satisfy these conditions except the first-order one. Extensive numerical experiments are also carried out to demonstrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear cancer invasion mathematical model with proliferation, growth and haptotaxis effects. We obtain lower bounds for the finite-time blow-up of solutions of the considered system with nonlinear diffusion operator when blow-up occurs. We have assumed both the Dirichlet and Neumann boundary conditions in R n , n ≥ 2 to attain the desire result. [ABSTRACT FROM AUTHOR]

We consider synchronization of the all-to-all power grid model with inertia and nonlinear terms of the first- and second-order derivatives. This model was derived from the energy conservation law in [G. Filatrella, A. H. Nielsen, and N. F. Pedersen, Eur. Phys. J. B, 61 (2008), pp. 485-491]. Since the model contains a nonlinear differential operator, we cannot use a Lyapunov functional and an a priori estimate method directly. In this paper, we provide a new framework to obtain complete phase and frequency synchronization of the power grid model. We assume that the coupling strength and the moment of inertia are positive and the initial data are near the synchronization state. After applying an appropriate transform, we derive a system of differential equations whose coefficient matrix is negative definite. The initial data assumption and the negative definite coefficient matrix lead to the global existence and synchronization of the power grid model with a nonlinear differential operator. For both identical and nonidentical cases, the exponential decay for the frequency difference is determined and the square of frequencies converges to the average of the normalized energy feeding rates. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear fractional-order PI (NL-FO-PI) controller is proposed for primary frequency control (PFC) of a wind farm based on the squirrel cage induction generator. The new structure composites a fractional-order operator and nonlinear function to achieve better control performance for the PFC system. The benchmarking process is demonstrated by investigating the performance of fractional-order PI (FO-PI) and nonlinear PI (NL-PI) controllers. Initially, the controller is applied to a single-area power system for design and stability study and then extended to the two-area interconnected wind farm to validate the applicability in the more realistic power system. The proposed control method ensures the balance of power and keeps the system frequency within a suitable range. The simulation results demonstrate that the proposed NL-FO-PI controller provides less percentage overshoot, settling time, rise time, and peak time than other controllers. [ABSTRACT FROM AUTHOR]

In this paper we study existence, nonexistence and classification of radial positive solutions of some weighted fully nonlinear equations involving Pucci extremal operators. Our results are entirely based on the analysis of the dynamics induced by an autonomous quadratic system which is obtained after a suitable transformation. This method allows to treat both regular and singular solutions in a unified way, without using energy arguments. In particular we recover known results on regular solutions for the fully nonlinear non weighted problem by alternative proofs. We also slightly improve the classification of the solutions for the extremal operator M −. [ABSTRACT FROM AUTHOR]

Nonlinear grey Bernoulli model, abbreviated as NGBM model, has been validly used in real applications due to its high accuracy in nonlinear time series forecasting. However, there remain technical challenges to explain the mechanism of the accumulative sum operator in nonlinear grey modelling process and estimate structural parameters independent from the initial values. This paper aims to reconstruct the modelling process of the NGBM model so as to explain the modelling mechanism better by utilizing the integral matching approach, which consists of an integral formula and the numerical discretization-based least squares. First, the integral formula is employed to investigate the accumulative sum operator and further reconstruct the NGBM model to a generalized form, referred as to INGBM model. Then, a novel parameter estimation strategy, estimating structure parameters and initial values simultaneously, is developed by utilizing the numerical discretization-based least squares approach. Next, Monte Carlo simulation studies are designed to evaluate the finite sample performance of both models. Comparisons show that the INGBM model outperforms to the original one in terms of parameter estimation accuracy, forecasting accuracy and robustness to noise. Finally, we apply the INGBM model at a coal consumption in China study to further illustrate the usefulness of this model. [ABSTRACT FROM AUTHOR]

In the current work, we present some innovative solutions for the attractivity of fractional functional q-differential equations involving Caputo fractional q-derivative in a k-dimensional system, by using some fixed point principle and the standard Schauder's fixed point theorem. Likewise, we look into the global attractivity of fractional q-differential equations involving classical Riemann-Liouville fractional q-derivative in a k-dimensional system, by employing the famous fixed point theorem of Krasnoselskii. Also, we must note that, this paper is mainly on the analysis of the model, with numerics used only to verify the analysis for checking the attractivity and global attractivity of solutions in the system. Lastly, we give two examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we study the horizontal Newton transformations, which are nonlinear operators related to the natural splitting of the second fundamental form for hypersurfaces in a complex space form. These operators allow to prove the classical Minkowski formulas in the case of real space forms: unlike the real case, the horizontal ones are not divergence-free. Here, we consider the highest order of nonlinearity and we will show how a Minkowski-type formula can be obtained in this case. [ABSTRACT FROM AUTHOR]

In the present paper, we study infinite dimensional orthogonality preserving the second-order nonlinear Markov operators. It is proved that subjectivity of the second-order nonlinear Markov operators is equivalent to the orthogonality preserves in the class of π-Volterra operators. Moreover, a full description of such kind of operators has been found in terms of heredity coefficients. Besides, we are able to represent these operators their canonical forms. Furthermore, some properties of orthogonality preserving the second-order nonlinear operators and their fixed points are studied. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of solutions to a class of p(x)-Kirchhoff-type equations with Robin boundary data as follows: − M ∫ Ω 1 p (x) ∇ u p (x) d x + ∫ ∂ Ω β (x) p (x) ∇ u p (x) d σ div( ∇ u p(x)-2 ∇ u)=f(x,u)in Ω , ∇ u p (x) − 2 ∂ u ∂ v + β (x) u p (x) − 2 u = 0 on ∂ Ω , Where β ∈ L ∞ (∂ Ω) and f : Ω × ℝ → ℝ satisfies Carathéodory condition. By means of variational methods and the theory of the variable exponent Sobolev spaces, we establish conditions for the existence of weak solutions. [ABSTRACT FROM AUTHOR]

In this work successive differentiation method is applied to solve highly nonlinear partial differential equations (PDEs) such as Benjamin-Bona-Mahony equation, Burger's equation, Fornberg-Whitham equation, and Gardner equation. To show the efficacy of this new technique, figures have been incorporated to compare exact solution and results of this method. Wave variable is used to convert the highly nonlinear PDE into ordinary differential equation with order reduction. Then successive differentiation method is utilized to obtain the numerical solution of considered PDEs in this paper. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with the existence and approximate controllability for a class of fractional nonlocal control systems governed by abstract fractional evolution equations with multiple delays. Under some weaker assumptions, the existence as well as the approximate controllability is established by using fixed point theory. An example is given to illustrate the applicability of the abstract results. [ABSTRACT FROM AUTHOR]

This paper proposes a first-order algorithm for unconstrained nonlinear optimal control problems based on the fixed point theorem. The method has the following features: (a) the algorithm is simple; (b) unlike second-order algorithms, the choice of the first approximation is less critical; and (c) unlike gradient methods, experimental selections of parameters during iterative calculations are not required. This paper also describes the conditions of convergence of the algorithm in the space of continuous functions, and the optimality of a solution derived. [ABSTRACT FROM AUTHOR]

• A Deep Operator Network (DeepONet) for data-driven transient response prediction. • The Bayesian DeepONet enables a reliable prediction via uncertainty quantification. • The Bayesian DeepONet enables learning even when data is scarce. • The Probabilistic DeepONet enables a reliable prediction at virtually no extra cost This paper proposes a novel data-driven method for the reliable prediction of the power grid's post-fault trajectories, i.e., the power grid's dynamic response after a disturbance or fault. The proposed method is based on the recently proposed concept of Deep Operator Networks (DeepONets). Unlike traditional neural networks that learn to approximate functions, DeepONets are designed to approximate nonlinear operators, i.e., mappings between infinite-dimensional spaces. Under this operator framework, we design a novel and efficient DeepONet that (i) takes as inputs the trajectories collected before and during the fault and (ii) outputs the predicted post-fault trajectories. In addition, we endow our method with the much-needed ability to balance efficiency with reliable/trustworthy predictions via uncertainty quantification. To this end, we propose and compare two novel methods that enable quantifying the predictive uncertainty. First, we propose a Bayesian DeepONet (B-DeepONet) that uses stochastic gradient Hamiltonian Monte-Carlo to sample from the posterior distribution of the DeepONet trainable parameters. Then, we design a Probabilistic DeepONet (Prob-DeepONet) that uses a probabilistic training strategy to enable quantifying uncertainty at virtually no extra computational cost. Finally, we validate the proposed methods' predictive power and uncertainty quantification capability using the New York-New England power grid model. [ABSTRACT FROM AUTHOR]

Many applications, such as system identification, classification of time series, direct and inverse problems in partial differential equations, and uncertainty quantification lead to the question of approximation of a non-linear operator between metric spaces X and Y. We study the problem of determining the degree of approximation of such operators on a compact subset K X ⊂ X using a finite amount of information. If F : K X → K Y , a well established strategy to approximate F (F) for some F ∈ K X is to encode F (respectively, F (F)) in terms of a finite number d (respectively m) of real numbers. Together with appropriate reconstruction algorithms (decoders), the problem reduces to the approximation of m functions on a compact subset of a high dimensional Euclidean space R d , equivalently, the unit sphere S d embedded in R d + 1. The problem is challenging because d , m , as well as the complexity of the approximation on S d are all large, and it is necessary to estimate the accuracy keeping track of the inter-dependence of all the approximations involved. In this paper, we establish constructive methods to do this efficiently; i.e., with the constants involved in the estimates on the approximation on S d being O (d 1 / 6). We study different smoothness classes for the operators, and also propose a method for approximation of F (F) using only information in a small neighborhood of F , resulting in an effective reduction in the number of parameters involved. To further mitigate the problem of large number of parameters, we propose prefabricated networks, resulting in a substantially smaller number of effective parameters. The problem is studied in both deterministic and probabilistic settings. [ABSTRACT FROM AUTHOR]

In this paper we suggest an enhanced Geraghty-type contractive mapping for examining the existence properties of classical nonlinear operators with or without prior degenerates. The nonlinear operators are proved to exist with the imposition of the Geraghty-type condition in a non-empty closed subset of complete metric spaces. To showcase some efficacies of the Geraghty-type condition, convergent rate and stability are deduced. The results are used to study some asymptotic properties of perturbed integral and hypergeometric operators. The results also extend and generalize some existing Geraghty-type conditions. [ABSTRACT FROM AUTHOR]

The paper proposes a new class of nonlinear operators and a dual learning paradigm where optimization jointly concerns both linear convolutional weights and the parameters of these nonlinear operators. The nonlinear class proposed to perform a rich functional representation is composed by functions called rectified parametric sigmoid units. This class is constructed to benefit from the advantages of both sigmoid and rectified linear unit functions, while rejecting their respective drawbacks. Moreover, the analytic form of this new neural class involves scale, shift and shape parameters to obtain a wide range of activation shapes, including the standard rectified linear unit as a limit case. Parameters of this neural transfer class are considered as learnable for the sake of discovering the complex shapes that can contribute to solving machine learning issues. Performance achieved by the joint learning of convolutional and rectified parametric sigmoid learnable parameters are shown to be outstanding in both shallow and deep learning frameworks. This class opens new prospects with respect to machine learning in the sense that main learnable parameters are attached not only to linear transformations, but also to a wide range of nonlinear operators. [ABSTRACT FROM AUTHOR]

In the present paper we consider a genetic algebra induced by b−bistochastic Quadratic Stochastic Operators (QSOs) which is called b−bistochastic genetic algebra. First, we characterize their nontrivial character function on Rn. It turns out that, the given character function is not unique, hence full descriptions of such functions on R¹ and R² are established. Moreover, the defined algebra is commutative but not associative in general, hence, the associativity of b−bistochastic genetic algebras defined on R¹ and R² are described. In this work, the existence of non-trivial derivations on such algebras are given. [ABSTRACT FROM AUTHOR]

This paper deals with evolutionary algorithms for solving the vehicle routing problem. More precisely, the paper is concerned with eight evolutionary crossover operators, which have originally been designed for the traveling salesman problem but can also be used for vehicle routing. The considered crossovers are tested on a set of well known benchmark problem instances. The obtained experimental results clearly show that the behavior and relative ranking of the operators within the vehicle routing environment is different than within the traveling salesman environment. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of fractional boundary value problems with the derivative term and nonlinear operator term. By establishing new mixed monotone fixed point theorems, we prove these problems to have a unique solution, and we construct the corresponding iterative sequences to approximate the unique solution. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following non-linear equations in unbounded domains Ω with exterior Dirichlet condition: { (− Δ) p s u (x) = f (u (x)) , x ∈ Ω , u (x) > 0 , x ∈ Ω , u (x) = 0 , x ∈ R n ∖ Ω , where (− Δ) p s is the fractional p -Laplacian defined as (0.1) (− Δ) p s u (x) = C n , s , p P. V. ∫ R n | u (x) − u (y) | p − 2 [ u (x) − u (y) ] | x − y | n + s p d y with 0 < s < 1 and p ≥ 2. We first establish a maximum principle in unbounded domains involving the fractional p -Laplacian by estimating the singular integral in (0.1) along a sequence of approximate maximum points. Then, we obtain the asymptotic behavior of solutions far away from the boundary. Finally, we develop a sliding method for the fractional p -Laplacians and apply it to derive the monotonicity and uniqueness of solutions. There have been similar results for the classical Laplacian [3] and for the fractional Laplacian [39] , which are linear operators. Unfortunately, many approaches there no longer work for the fully non-linear fractional p -Laplacian here. To circumvent these difficulties, we introduce several new ideas, which enable us not only to deal with non-linear non-local equations, but also to remarkably weaken the conditions on f (⋅) and on the domain Ω. We believe that the new methods developed in our paper can be widely applied to many problems in unbounded domains involving non-linear non-local operators. [ABSTRACT FROM AUTHOR]

We consider an elliptic variational-hemivariational inequality 𝓟 in a reflexive Banach space, governed by a set of constraints K, a nonlinear operator A, and an element f. We associate to this inequality a sequence {𝓟n} of variational-hemivariational inequalities such that, for each n ∈ ℕ, inequality 𝓟n is obtained by perturbing the data K and A and, moreover, it contains an additional term governed by a small parameter εn. The unique solvability of 𝓟 and, for each n ∈ ℕ, the solvability of its perturbed version 𝓟n, are guaranteed by an existence and uniqueness result obtained in literature. Denote by u the solution of Problem 𝓟 and, for each n ∈ ℕ, let un be a solution of Problem 𝓟n. The main result of this paper states the strong convergence of un → u in X, as n → ∞. We show that the main result extends a number of results previously obtained in the study of Problem 𝓟. Finally, we illustrate the use of our abstract results in the study of a mathematical model which describes the contact of an elastic body with a rigid-deformable foundation and provide the corresponding mechanical interpretations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of cyclic p-contraction pair for single-valued mappings. Then we present some best proximity point results for such mappings defined on proximally complete pair of subsets of a metric space. Also, we provide some illustrative examples that compared our results with some earliest. Finally, by taking into account a fixed point consequence of our main result we give an existence and uniqueness result for a common solution of a system of second order boundary value problems. [ABSTRACT FROM AUTHOR]

In this paper we study to what extent properties of the classical linear Volterra operators can be transferred to the nonlinear Volterra– Choquet operators, obtained by replacing the classical linear integral with respect to the Lebesgue measure, by the nonlinear Choquet integral with respect to a nonadditive set function. Compactness, Lipschitz and cyclicity properties are studied. [ABSTRACT FROM AUTHOR]

Nonlinear positive operators by means of maximum and product were introduced by B. Bede. In this paper, we introduce nonlinear maximum-product type modified Favard Szasz-Mirakyan operators. Our main purpose is to give a theorem on the rate of convergence. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce and study the concept of generalized fuzzy cone metric space and to obtain the topology by using G-fuzzy cone metric. Moreover, the existence of common fixed point theorem for contractive map and occasionally weakly compatible map and is investigated in generalized fuzzy cone metric space. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of weakly b - (φ,G) contraction mapping in b-metric spaces endowed with a graph and give some fixed point results for such contractions. [ABSTRACT FROM AUTHOR]

We present an operator calculus based on Krawtchouk polynomials, including Krawtchouk transforms and corresponding convolution structure which provides an inherently discrete alternative to Fourier analysis. This approach is well suited for applications such as digital image processing. This paper includes the theoretical aspects and some basic examples. [ABSTRACT FROM AUTHOR]

In this paper, we show how the global bifurcation theory for nonlinear Fredholm operators (Theorem 4.3 of [Shi & Wang, 2009]) and for compact operators (Theorem 1.3 of [Rabinowitz, 1971]) can be used in the study of the nonconstant stationary solutions for a volume-filling chemotaxis model with logistic growth under Neumann boundary conditions. Our results show that infinitely many local branches of nonconstant solutions bifurcate from the positive constant solution (u c , α β u c) at χ = χ ¯ k . Moreover, for each k ≥ 1 , we prove that each Γ k can be extended into a global curve, and the projection of the bifurcation curve Γ k onto the χ -axis contains ( χ ¯ k , ∞). [ABSTRACT FROM AUTHOR]