非线性算子的离散逼近和拓扑度

THE DISCRETE APPROXIMATIONS AND THE TOPOLOGICAL DEGREE FOR NONLINEAR OPERATORS

本文引入了较D-收敛广泛的广义D-收敛,然后利用这些概念,定义了A-regular映射,以及这类映射的广义拓扑度,它具有通常的多值拓扑度的性质.最后,证明了自反Banach空间上的(S)型单调映射可以归结为A-regular映射.

This paper is divided into two parts. In the first part, the concept of Stummcl's D-convergcncc is extended to the concept of generalized D-convcrgcnce, then usmg these concepts, the author introduces the class of A-regular mappings which arc a natural class to considering approximation-solvability and more general than A-proper mappings, at last a generalized topological degree for A-rcgular mappjngs is obtained, this degree has properties analogous to those of the degree for A-propcr mappings. In the second part, it is shown that the monotone mappings of type (s) in a reflexive Banach space arc A-rcgular mappings, this develops Browder's result.