Accession Number:
AD0735835
Title:
Fixed Points and Stability for a Sum of Two Operators in Locally Convex Spaces
Descriptive Note:
Technical summary rept.
Corporate Author:
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
Personal Author(s):
Report Date:
1971-09-01
Pagination or Media Count:
28.0
Abstract:
Some fixed point theorems for a sum of two operators are proved, generalizing to locally convex spaces a fixed point theorem of M. A. Krasnoselskii, for a sum of a completely continuous and a contraction mapping, as well as some of its recent variants. A notion of stability of solutions of nonlinear operator equations in linear topological spaces is formulated in terms of specific topologies on the set of nonlinear operators, and a theorem on the stability of fixed points of a sum of two operators is given. As a byproduct, sufficient conditions for a mapping to be open or to be onto are obtained.
Descriptors:
Subject Categories:
- Theoretical Mathematics