Zhang Shi-sheng

Some existence theorems of common and coincidence solutions for a class of systems of functional equations arising in dynamic programming

Some existence theorems of common and coincidence solutions for a class of more general systems of functional equations arising in dynamic programming are shown. The results presented in this paper not only contain the corresponding results of [6,7] as special cases, but also give an existence theorem of solutions for a class of functional equations suggested by Wang[2–5] recently.

Degree theory for multivalued (S) type mappings and fixed point theorems

AbstractThe main purpose of this paper is devoted to generalizing the results of Browder[1,2]. This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S) type mappings and the concepts of the limits of multivalued (S) and (S) type mappings. These kinds of mappings contain many monotone type mappings, such as maximal monotone mapping, bounded pseudo-monotone mapping and bounded generalized pseudo-monotone mapping, as its special cases. In the second part we define the pseudo-degree for (S) type mapping and the degree for (S)+type mapping. These two kinds of degrees are all the generalizations of the degree defined by Browder[1,2].As applications, we utilize the degree theory presented in part 2 to study the existence of solutions for the multivalued operator equations (see part 3) and to obtain some new fixed point theorems in part 4.

Strong convergence theorems for nonexpansive semi-groups in Banach spaces

Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of Shioji-Takahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.

Topological degree theory and fixed point theorems in probabilistic metric spaces

The Leray-Schauder topological degree theory is established in the probabilistic linear normed spaces. Based on this theory, some fixed point theorems for mappings in the probabilistic linear normed spaces are shown.The Leray-Schauder topological degree theory is established in the probabilistic linear normed spaces. Based on this theory, some fixed point theorems for mappings in the probabilistic linear normed spaces are shown.

Ekeland's variational principle and Caristi's fixed point theorem in probabilistic metric space

The main purpose of this paper is to establish the Ekelands variational principle and Caristis fixed point theorem in probabilistic metric spaces and to give a direct simple proof of the equivalence between these two theorems in the probabilistic metric space. The results presented in this paper generalize the corresponding results of [9–12].The main purpose of this paper is to establish the Ekelands variational principle and Caristis fixed point theorem in probabilistic metric spaces and to give a direct simple proof of the equivalence between these two theorems in the probabilistic metric space. The results presented in this paper generalize the corresponding results of [9–12].

On the degree theory for multivalued (S+) type mappings

This paper is to generalize the results of Zhang and Chen[1]. We construct a topological degree for a class of mappings of the form F=L+S where L is closed densely defined maximal monotones operator and S is a nonlinear multivalued map of class (S+) with respect to the domain of L.

Basic theory and applications of probabilistic metric spaces (II)

This paper is a continuation of the authors previous paper [1], in which the characterizations of various probabilistically bounded sets are presented, and the linear operator theory and fixed point theory on probabilistic metric spaces are given, too.

Some further generalizations of Ky Fan's minimax inequality and its applications to variational inequalities

The purpose of this paper is to introduce the concept of generalized KKM mapping and to obtain some general version of the famous KKM theorem and Ky Fans minimax inequality. As applications, we utilize the results presented in this paper to study the saddle point problem and the existence problem of solutions for a class of quasi-variational inequalities. The results obtained in this paper extend and improve some recent results of [1–6].

Existence and Approximation of Solutions to Variational Inclusions with Accretive Mappings in Banach Spaces

The purpose of this paper is to study the existence and approximation problem of solutions for a class of variational inclusions with accretive mappings in Banach spaces. The results extend and improve some recent results.The purpose of this paper is to study the existence and approximation problem of solutions for a class of variational inclusions with accretive mappings in Banach spaces. The results extend and improve some recent results.

On the existence and uniqueness of solutions for a class of variational inequalities with applications to the signorini problem in mechanics

In this paper, we introduce a new unified and general class of variational inequalities, and show some existence and uniqueness results of solutions for this kind of variational inequalities. As an application, we utilize the results presented in this paper to study the Signorini problem in mechanics.