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):

• Cain, Jr., G. L.
• Nashed, M. Z.

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:

• *FUNCTIONAL ANALYSIS
• NONLINEAR SYSTEMS
• OPERATORS(MATHEMATICS)
• MAPPING(TRANSFORMATIONS)
• HILBERT SPACE
• CONVEX SETS
• THEOREMS
• BANACH SPACE

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE