PRODUCTS OF RESOLVENTS AND MULTIVALUED HYBRID MAPPINGS IN C AT(0) SPACES

In this article, we introduce and investigate the concept of multivalued hybrid mappings in C AT（0） spaces by using the concept of quasilinearization. Also, we present a new iterative algorithm involving products of Moreau-Yosida resolvents for finding a common element of the set of minimizers of a finite family of convex functions and a common fixed point of two multivalued hybrid mappings in C AT（0） spaces.

On Positive Eigenvalues and Positive Fixed Points of Multivalued Condensing Mappings

In this paper,we discuss the calculations of fixed point indexs for multivalued condensing mappings and k-set-contraction mappings,obtain some theorems on the eigenvalues and the fixed points under the suitable conditions. Our conclusions improve and generalize some well-known results.

On Fixed Point and Almost Fixed Point Problems of Lower Semicontinuous Type Multivalued Mappings

In the present paper, some new almost fixed point theorems and fixed point theorems for lower semicontinuous type multivalued mappings are obtained in metrizable H-spaces.

Solvability of Impulsive Neutral Functional Differential Inclusions in Banach Spaces

Impulsive neutral differential inclusions play an important role in characterizing many social, physical and engineering problems, and the existence of solutions for the initial value problem in Banach spaces has been extensively studied. However, in most cases, the nonlinear term on the right-hand side of differential inclusions has to satisfy the compact or continuous assumptions. The object of this paper is to study the existence of solutions to the initial value problems of the first and second order impulsive neutral functional differential inclusions in Banach spaces under some weaker conditions, where the nonlinear term on the right-hand side does not necessarily satisfy the compact and continuous assumptions. Based on a fixed point theorem for discontinuous multivalued increasing operators, the results are obtained by means of the partial ordering method and measure of noncompactness.

OPTIMAL CONTROL OF HYPERBOLIC H-HEMIVARIATIONAL INEQUALITIES WITH STATE CONSTRAINTS

The optimal control problems of hyperbolic H-hemivariational inequalities with the state constraints and nonnomotone multivalued mapping term are considered.The optimal solutions are obtained.In addition,their approximating problems are also studied.

OPTIMAL CONTROL OF PARABOLIC VARIATIONAL INEQUALITIES WITH STATE CONSTRAINT

The optimal control problem of parabolic variational inequalities with the state constraint and nonlinear, discontinuous nonmonotone multivalued mapping term and its approximating problem are studied, which generalizes some obtained results.

SOME GENERALIZATIONS OF KY FAN'S BEST APPROXIMATION THEOREM

We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map on metrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derived for the map studied. Our work generalizes severl results in approximation theory.

Fixed Points of Multivalued Quasi-nonexpansive Mappings Using a Faster Iterative Process

In this article, we prove some strong and weak convergence theorems for quasi-nonexpansive multivalued mappings in Banach spaces. The iterative process used is independent of Ishikawa iterative process and converges faster. Some examples are provided to validate our results. Our results extend and unify some results in the contemporary literature.

A CLASS OF PARABOLIC HEMIVARIATIONAL INEQUALITIES

Quasilinear parabolic hemivariational inequalities as a generalization to nonconvex functions of the parabolic variational inequalities are discussed. This extension is strongly motivated by various problems in mechanics. By use of the notion of the generalized gradient of Clarke and the theory of pseudomonotone operators, it is proved there exists at least one solution.

A FIXED POINT THEOREM FOR MULTIVALUED NONEXPANSIVE MAPPINGS IN BANACH SPACES OF NORMAL STRUCTURE

Since the appearance of T. C. Lim’s fixed point theorem for multivalued nonexpansive mappings in uniformly convex spaces in 1974, various generalizations and modifications have been obtained (e.g. [2, 3] and other references in [4, 5]). However, the corresponding fixed point problem for Banach spaces of normal structure remains open. The present report shall give a positive answer to it.

Fixed points of n-valued maps on surfaces and the Wecken property a configuration space approach

Abstract In this paper, we explore the fixed point theory of n-vaiued maps using configuration spaces and braid groups, focusing on two fundamental problems, the Wecken property, and the computation of the Nielsen number. We show that the projective plane （resp. the 2-sphere S2） has the Wecken property for n-valued maps for all n ∈N （resp. all n ≥ 3）. In the case n = 2 and S2, we prove a partial result about the Wecken property. We then describe the Nielsen number of a non-split n-valued map φ ： X → X of an orientable, compact manifold without boundary in terms of the Nielsen coincidence numbers of a certain finite covering q： ）→ X with a subset of the coordinate maps of a lift of the n-valued split map → q ： →X.

ON A KIND OF GENERALIZED QUASI-VARIATIONAL INEQUALITIES AND FAN's MINIMAX INEQUALITY WITHOUT CONVEXITY

This Paper gives a Fan’s type minimax theorem, a nearest point theorem and two existence theorems of solutions for a kind of generalized quasi-variational inequalities in H-spaces without any linear structure.