多值(S)型映象度理论以及不动点定理

基金项目: 国家自然科学基金资助课题

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

摘要: 本文的主要目的是推广Browder^[1,2]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^[1,2]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.

Abstract: The 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.

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