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.

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE