Abstract and Applied Analysis
Volume 2003 (2003), Issue 12, Pages 685-696
Approximation structures and applications to evolution equations
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 -proper operators as well as a generalized Leray-Schauder principle. Also, a method of approximating arbitrary continuous operators by -proper mappings is described. We construct, via appropriate Browder-Petryshyn approximation schemes, approximative solutions for linear evolution equations in Banach spaces.