Abstract and Applied Analysis
Volume 2003 (2003), Issue 12, Pages 685-696
doi:10.1155/S1085337503301010

Approximation structures and applications to evolution equations

Abstract

We discuss various properties of the nonlinear A-proper operators as well as a generalized Leray-Schauder principle. Also, a method of approximating arbitrary continuous operators by A-proper mappings is described. We construct, via appropriate Browder-Petryshyn approximation schemes, approximative solutions for linear evolution equations in Banach spaces.