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This paper is devoted to numerical analysis of a new class of elliptic variational–hemivariational inequalities in the study of a family of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contact condition and the friction is modeled by a nonmonotone multivalued subdifferential relation allowing slip dependence. The problem involves a nonlinear elasticity operator, the subdifferential of the indicator function of a convex set for the locking constraints and a nonconvex locally Lipschitz friction potential. Solution existence and uniqueness result on the inequality can be found in Migórski and Ogorzaly (2017). In this paper, we introduce and analyze a finite element method to solve the variational–hemivariational inequality. We derive a Céa type inequality that serves as a starting point of error estimation. Numerical results are reported, showing the performance of the numerical method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a dual-mixed formulation for stationary viscoplastic flows with yield, such as the Bingham or the Herschel-Bulkley flow. The approach is based on a Huber regularization of the viscosity term and a two-fold saddle point nonlinear operator equation for the resulting weak formulation. We provide the uniqueness of solutions for the continuous formulation and propose a discrete scheme based on Arnold-Falk-Winther finite elements. The discretization scheme yields a system of slantly differentiable nonlinear equations, for which a semismooth Newton algorithm is proposed and implemented. Local superlinear convergence of the method is also proved. Finally, we perform several numerical experiments in two and three dimensions to investigate the behavior and efficiency of the method. [ABSTRACT FROM AUTHOR]

This paper presents the numerical analysis for a variant of the nonlinear multiscale Dynamic Diffusion (DD) method for the advection-diffusion-reaction equation initially proposed by Arruda et al. [1] and recently studied by Valli et al. [2]. The new DD method, based on a two-scale approach, introduces locally and dynamically an extra stability through a nonlinear operator acting in all scales of the discretization. We prove existence of discrete solutions, stability, and a priori error estimates. We theoretically show that the new DD method has convergence rate of O (h 1 / 2) in the energy norm, and numerical experiments have led to optimal convergence rates in the L 2 (Ω) , H 1 (Ω) , and energy norms. [ABSTRACT FROM AUTHOR]

Abstract: Let be a nonempty, closed and convex subset of a real Hilbert space . Let , be a finite family of generalized asymptotically nonexpansive mappings. It is our purpose, in this paper to prove strong convergence of Mann’s type method to a common fixed point of provided that the interior of common fixed points is nonempty. No compactness assumption is imposed either on or on . As a consequence, it is proved that Mann’s method converges for a fixed point of nonexpansive mapping provided that interior of . The results obtained in this paper improve most of the results that have been proved for this class of nonlinear mappings. [Copyright &y& Elsevier]

Abstract: This paper deals with the second order nonlinear neutral delay difference equation By using Krasnoselskii’s fixed point theorem and some new techniques, we obtain the existence results of uncountably many bounded positive solutions for the above equation. Examples that cannot be solved by known results are given to illustrate the results presented in this paper. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce and study a new class of nonlinear random -resolvent operator equations with random relaxed cocoercive operators in Hilbert spaces. By using Chang’s lemma, Theorem 3.1 of Liu and Li, and the resolvent operator technique for -monotone operators due to Lan, we also prove the existence theorems of the solutions and convergence theorems of the new generalized random iterative procedures with errors for this nonlinear random -resolvent operator equations involving non-monotone random set-valued operators in Hilbert spaces. The results presented in this paper improve and generalize some known corresponding results in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, existence criteria of positive solutions to a class of nonlinear first-order periodic boundary value problems of impulsive dynamic equations on time scales are obtained. The main tool used in this paper is the well-known Guo–Krasnoselskii fixed-point theorem. [Copyright &y& Elsevier]

Abstract: In this paper, existence criteria for three positive solutions of -Laplacian difference equation are established by using the Five Functionals Fixed Point Theorem. As an application, one example is given to illustrate the main result in this paper. [Copyright &y& Elsevier]

In this paper we consider the first order evolutionary inclusions with nonlinear weakly continuous operators and a multivalued term which involves the Clarke subgradient of a locally Lipschitz function. First, we provide a surjectivity result for stationary inclusion with weakly–weakly upper semicontinuous multifunction. Then, we use this result to prove the existence of solutions to the Rothe sequence and the evolutionary subgradient inclusion. Finally, we apply our results to the non-stationary Navier–Stokes equation with nonmonotone and multivalued frictional boundary conditions. [ABSTRACT FROM AUTHOR]

Abstract: In 2010, Kadelburg et al. () by providing an example showed that a contraction in an ordered metric space is not necessarily a contraction (in the classical sense). Thus fixed point results in ordered metric spaces are generalizations of ones in metric spaces in a sense. In this paper, we give some ordered fixed point results for convex contractions and special mappings which satisfy some contraction conditions. Also, we give some results concerning the property (P). [Copyright &y& Elsevier]

Abstract: The aim of this paper is to generalize two classical fixed point theorems given by Bogin [J. Bogin, A generalization of a fixed point theorem of Goebel, Kirk and Shimi, Canad. Math. Bull. 19 (1976) 7–12] and Greguš [M. Greguš, A fixed point theorem in Banach spaces, Boll. Un. Math. Ital. A (5) 17 (1980) 193–198]. We also complement and extend some very recent results proved by Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008) 1861–1869]. [Copyright &y& Elsevier]

Abstract: Recently, Bucur, Guran and Petrusel presented some results on fixed points of multivalued operators on generalized metric spaces which extended some old fixed point theorems to the multivalued case (Bucur et al., 2009 ). Also, Kikkawa and Suzuki have proved some results for generalized contractions in complete metric spaces (Kikkawa, 2008 ). In this paper, we shall give some results on fixed points of multivalued operators on generalized metric spaces by using the method of Kikkawa (2008) . [Copyright &y& Elsevier]

Abstract: We develop a multilevel augmentation method for solving nonlinear boundary value problems. We first describe the multilevel augmentation method for solving nonlinear operator equations of the second kind which has been proposed in our recent paper Chen et al. (2011) , and then apply it to solving the nonlinear two-point boundary value problems of second-order differential equations. The theoretical analysis of convergence order and computational complexity are proposed. Finally numerical experiments are presented to confirm the theoretical estimates and illustrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we extend a fixed point theorem of Imdad and Kumar, for a pair of non-self maps, to non-normal cone spaces. [Copyright &y& Elsevier]

Abstract: In this paper, by using Krasnoselskii’s Fixed Point Theorem in a cone, we study the existence of positive solutions for the second-order three-point boundary value problem where and is allowed to change sign. We also give some examples to illustrate our results. [Copyright &y& Elsevier]

Abstract: This paper is devoted to studying the uniqueness problem of entire functions sharing one value or fixed points. We improve some results given by Fang and extend some results given by Fang and Qiu and by Lin and Yi. [Copyright &y& Elsevier]

Abstract: By applying the well-known Leggett–Williams multiple fixed point theorem, this paper investigates the existence of multiple positive periodic solutions of functional differential equations with impulses and a parameter. [Copyright &y& Elsevier]

Abstract: In this paper, we consider some kind of nonlinear periodic differential equation with impulses on time scales, and give some new criteria for the existence of at least one solution by using differential inequalities and fixed point theorems. [Copyright &y& Elsevier]

Abstract: In this paper, by using the Sadovskii fixed point theorem, we study the existence of at least one solution for the second-order three-point boundary value problem in a Banach space , where is the zero element of . We also obtain the existence of at least one positive solution. As an application, we give an example to demonstrate our results. [Copyright &y& Elsevier]

In this paper, by using the fixed point theory, under quite general conditions on the nonlinear term we obtain a existence result of unbounded positive solutions of Schrödinger equations in two-dimensional exterior domains. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the existence of multiple positive solutions for multi-point boundary value problems with a one dimensional -Laplacian where . By the fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem. [Copyright &y& Elsevier]

The goal of this paper is to study the existence and uniqueness of positive solutions for the th order boundary value problem: The Krein–Rutman theorem and the Krasnoselskii–Zabreiko fixed point theorem are the main tools that have been used to develop our work. [Copyright &y& Elsevier]

In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings. The result is applied to prove the existence of solution of system of nonlinear integral equations. Our theorems extend and improve several known results. [Copyright &y& Elsevier]

In this paper, a general hybrid fixed point theorem for the strict monotone increasing multi-valued mappings in ordered Banach spaces is proved via measure of noncompactness and it is further applied to perturbed functional nonconvex differential inclusions for proving the existence results for the extremal solutions under mixed Lipschitz, compactness and strict monotonic conditions. [Copyright &y& Elsevier]

This paper is mainly concerned with the existence of solutions for first order dynamic inclusions on time scales with nonlocal initial conditions. By using Bohnenblust–Karlin’s fixed point theorem and Leray–Schauder nonlinear alternative for multivalued maps, some sufficient conditions are established. An example is also included to illustrate our results. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a new class of iterative procedures with errors for approximating the common fixed point of two generalized asymptotically quasi-nonexpansive mappings and prove several strong convergence results for the iterative sequence with errors in Banach spaces. We not only answer the open question proposed by Zhou et al. [1], but also extend and improve some recent corresponding results in the literature. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the nonlinear fractional differential equation L(D)u=f(x,u), u(0)=0, 0<x<1, where L(D) = Ds n − a n−1 D s n−1 − … − a 1 D s 1 1 < s 2 < … < sn < 1, and aj > 0, j = 1,2,…, n − 1. Some results are obtained for the existence, nonexistence, and multiplicity of positive solutions of the above equation by using Krasnoselskii''s fixed-point theorem in a cone. In particular, it is proved that the above equation has N positive solutions under suitable conditions, where N is an arbitrary positive integer. [Copyright &y& Elsevier]

Abstract: In this paper, two multivalued versions of the well-known hybrid fixed-point theoremof Dhage [1] in Banach algebras are proved. As an application, an existence theorem for a certain differential inclusion in Banach algebras is proved. [Copyright &y& Elsevier]

Usually, man is infected with some kinds of epidemic disease since they live in a polluted environment [1–8], such as air pollution (e.g., pulmonary tuberculosis), or water pollution (e.g., snail fever). These kinds of toxicant are generated by polluted biological (e.g., degradation of forests, Creutzfeldt-Jakob disease result from bovine spongiform encephalopathy (BSE)), physical (e.g., nuclear radiation, syndrome of the Gulf War), or chemical environment (e.g., petroleum leaking, dioxin event in Belgium). As we know, the environmental pollution has been a very serious global problem, which may influence the spread of infectious diseases, and hence, has big effects on human health. In this paper, we study an SIS (susceptible/infected/susceptible) epidemic model with toxicology, using the Brouwer fixed-point theorem we show the existence of periodic solution of such a system, we also prove the global attraction of this solution, and we obtain the threshold between extinction and weakly persistent for the infected class. [Copyright &y& Elsevier]