Abstract and Applied Analysis
Volume 2003 (2003), Issue 12, Pages 685-696

Approximation structures and applications to evolution equations

Adrian Duma and Cristian Vladimirescu

Department of Mathematics, University of Craiova, Craiova 1100 , Romania

Received 29 October 2002

Copyright © 2003 Adrian Duma and Cristian Vladimirescu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.