Fixed Points and Stability for a Sum of Two Operators in Locally Convex Spaces

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.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1971
Accession Number
AD0735835

Entities

People

  • G. L. Cain Jr.
  • M. Z. Nashed

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Banach Space
  • Contracts
  • Convex Sets
  • Equations
  • Functional Analysis
  • Hilbert Space
  • Integral Equations
  • Mathematics
  • Perturbations
  • Plastic Explosives
  • Point Theorem
  • Real Numbers
  • Theorems
  • Topology
  • United States
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Linear Algebra

Technology Areas

  • Space