多值(S)型映象度理论以及不动点定理

Degree Theory for Multivalued (S) Type Mappings and Fixed Point Theorems

本文的主要目的是推广Browder的结果. 本文分四部分,首先我们介绍多值(S)及其(S)_+型映象以及多值(S),(S)_+型极限映象.它们包含许多单调型映象为特例,如极大单调映象.有界伪单调以及有界广义伪单调映象.在第二部分我们定义(S)型映象的伪度以及(S)_+映象的度,它们是Browder中度的推广。作为应用,我们利用第二部分中的度理论来研究多值算子方程解的存在性(见第三节),获得一些新的不动点定理.

The main purpose of this paper is devoted to generalizing the results of Brow-der[t, ]. 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.