Existence and continuous dependence results for nonlinear differential inclusions with infinite delay

This paper is concerned with nonlinear functional differential inclusions with infinite delay in Banach spaces. Using tools involving the measure of noncompactness and multi-valued fixed point theory, existence and continuous dependence results are obtained, for integral solutions, without the assumption of compactness on the associated nonlinear semigroup.     

Mann and Ishikawa-Type Iterative Schemes for Approximating Fixed Points of Multi-valued Non-Self Mappings

A Mann-type iterative scheme which converges strongly to a fixed point of a multi-valued nonexpansive non-self mapping T is constructed in a real Hilbert space H. We also constructed a Mann-type sequence which converges to a fixed point of a multi-valued quasi-nonexpansive non-self mapping under appropriate conditions. In addition, an Ishikawa-type iterative scheme which approximates the fixed points of multi-valued Lipschitz pseudocontractive non-self mappings is constructed in Banach spaces. The results obtained in this paper improve and extend the known results in the literature.

     

Existence results for impulsive hyperbolic differential inclusions

In this article we investigate the existence of solutions for second order impulsive hyperbolic differential inclusions in separable Banach spaces. By using suitable fixed point theorems, we study the case when the multi-valued map has convex and non-convex values.     

Existence theorems for solutions of variational inequalities

Summary The existence of nonzero solutions for a class of generalized variational inequalities is studied by fixed point index approach for multi-valued mappings in finite dimensional spaces and reflexive Banach spaces.     

序Banach空间中集值混合单调映象的耦合不动点定理

在序Banach空间中,研究了一类集值混合单调映象,用不同方法证明了两个新的耦合不动点存在性定理,所做工作扩充了文[5]的研究成果.     

Banach空间中多值Φ-增生和多值Φ-伪压缩映象的收敛定理

在任意Banach空间中引入比重要的多值-强增生映象和多值-强伪压缩映象更一般的多值Φ-增生映象和多值Φ-伪压缩映象,研究多值Φ-增生映象方程的解和多值Φ-伪压缩映象不动点的具随机误差的Ishikawa迭代逼近问题.这些结论推广和改进了最新文献中相应的结果.     

A hybrid extragradient method for solving pseudomonotone equilibrium problems using Bregman distance

In this paper, using a hybrid extragradient method, we introduce a new iterative process for approximating a common element of the set of solutions of equilibrium problems involving pseudomonotone bifunctions and the set of common fixed points of a finite family of multi-valued Bregman relatively nonexpansive mappings in the setting of reflexive Banach spaces. For this purpose, we introduce Bregman–Lipschitz-type condition for a pseudomonotone bifunction. It seems that these results for pseudomonotone bifunctions are first in reflexive Banach spaces. This paper concludes with certain applications, where we utilize our results to study the determination of a common point of the solution set of a variational inequality problem and the fixed point set of a finite family of multi-valued relatively nonexpansive mappings. A numerical example to support our main theorem will be exhibited.     

NONDENSELY DEFINED IMPULSIVE NEUTRAL FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH NONLOCAL CONDITIONS

In this paper,using a fixed point theorem for condensing multi-valued maps,we investigate the existence of integral solutions to a class of nondensely defined neutral evolution impulsive differential inclusions with nonlocal conditions in Banach spaces.     

微分包含的非线性边值问题

基于 Marteli 定理^[8], 该文得到了一个新的不动点定理,利用这一结果,作者给出了在Banach空间中的多值微分包含的非线性边值问题的解的存在性的充分条件.     

Φ-伪压缩映象带混合型误差的迭代序列的强稳定性

引入带混合型误差的 Ishikawa和 Mann迭代序列 ,在没有 D是有界闭集与多值映象 T是一致连续的较弱条件下 ,在实 Banach空间中研究了多值Φ -伪压缩映象不动点的带混合型误差的 Ishikawa和 Mann迭代序列的逼近问题 ,使用与文献完全不同的方法 ,建立了带混合型误差的 Ishikawa和 Mann迭代序列的强稳定性定理 ,从而统一和发展了几位作者早期与最近的相关结果 .     

On the convergence of a new iterative algorithm of three infinite families of generalized nonexpansive multi-valued mappings

In this paper, we establish some weak and strong convergence theorems for a new iterative algorithm under some suitable conditions to approximate the common fixed point of three infinite families of multi-valued generalized nonexpansive mappings in a uniformly convex Banach spaces. Our results generalize and improve several previously known results of the existing literature.     

An implicit iteration process for solving a fixed point problem of a finite family of multi-valued mappings in Banach spaces

This work is concerned with the strong convergence of an approximating common fixed point sequence of a finite family of multi-valued mappings in a uniformly convex and smooth Banach space using an implicit iteration scheme introduced by Xu and Ori [H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001) 767–773].     

Some results for fractional boundary value problem of differential inclusions

In this paper, we study fractional differential inclusions with Dirichlet boundary conditions. We prove the existence of a solution under both convexity and nonconvexity conditions on the multi-valued right-hand side. The proofs rely on nonlinear alternative Leray–Schauder type, Bressan–Colombo selection theorem and Covitz and Nadler’s fixed point theorem for multi-valued contractions. The compactness of the set solutions and relaxation results is also established. In the last section we consider the fractional boundary value problem with infinite delay.     

An iterative procedure for solving the common solution of two total quasi-ϕ-asymptotically nonexpansive multi-valued mappings in Banach spaces

In this paper, we introduce a new iterative procedure which is constructed by the shrinking hybrid projection method for solving the common solution of fixed point problems for two total quasi-?-asymptotically nonexpansive multi-valued mappings. Under suitable conditions, the strong convergence theorems are established in a uniformly smooth and strictly convex real Banach space with Kadec-Klee property. Our result improves and extends the corresponding ones announced by some authors.     

Controllability of Second Order Semi-Linear Neutral Functional Differential Inclusions in Banach Spaces

In this article, we investigate sufficient conditions for controllability of second order semi-linear neutral functional initial value problem for the class of differential inclusions in Banach spaces using the theory of strongly continuous cosine families. We shall rely on a fixed point theorem due to Ma for multi-valued maps. An example is provided to illustrate the result. This work is motivated by the paper of Benchohra, Gorniewicz and Ntouyas [7].In honour of Prof. M.C. Joshi, IIT Bombay, INDIA.     

Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings

In this paper, the famous Banach contraction principle and Caristi's fixed point theorem are generalized to the case of multi-valued mappings. Our results are extensions of the well-known Nadler's fixed point theorem [S.B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969) 475-487], as well as of some Caristi type theorems for multi-valued operators, see [N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989) 177-188; J.P. Aubin, Optima and Equilibria. An Introduction to Nonlinear Analysis, Grad. Texts in Math., Springer-Verlag, Berlin, 1998, p. 17; S.S. Zhang, Q. Luo, Set-valued Caristi fixed point theorem and Ekeland's variational principle, Appl. Math. Mech. 10 (2) (1989) 111-113 (in Chinese), English translation: Appl. Math. Mech. (English Ed.) 10 (2) (1989) 119-121], etc.     

Common fixed point theorem for cyclic generalized multi-valued contraction mappings

In this paper, we extend a multi-valued contraction mapping to a cyclic multi-valued contraction mapping. We also establish the existence of common fixed point theorem for a cyclic multi-valued contraction mapping. Our results extend, generalize and unify Nadler’s multi-valued contraction mapping and many fixed point theorems for multi-valued mappings.     

Convergence of an iterative method for relatively nonexpansive multi-valued mappings and equilibrium problems in Banach spaces

In this paper, an iterative sequence for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of two relatively nonexpansive multi-valued mappings is introduced. This iterative scheme can be viewed as a multi-valued version of the corresponding one introduced by Zhang et al. (Comput Math Appl 61, 262–276, 2011) for two relatively nonexpansive multi-valued mappings. Finally, strong convergence of this sequence is studied in Banach spaces.     

Algorithms for a system of generalized mixed equilibrium problems and a countable family of some nonlinear multi-valued nonexpansive-type maps

In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halperntype that approximate a solution of a system of a generalized mixed equilibrium problem and a common fixed point of a countable family of totally quasi-φ-asymptotically nonexpansive multi-valued maps are constructed. Strong convergence of the sequence generated by these algorithms is proved in uniformly smooth and strictly convex real Banach spaces with KadecKlee property. Furthermore, several applications of our theorems are also presented. Finally,our theorems are significant improvements on several important recent results for this class of nonlinear problems.     

Krasnoselskii type fixed point theorems for multi-valued mappings with weakly sequentially closed graph

In this work, using an analogue of Sadovskii’s fixed point result for multi-valued mappings with weakly sequentially closed graph, we prove new multi-valued analogues of Krasnoselskii fixed point theorem for mappings with weakly sequentially closed graph and under weak topology features. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness.