Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 635030, 13 pages
doi:10.1155/2011/635030
Research Article

Variational-Like Inclusions and Resolvent Equations Involving Infinite Family of Set-Valued Mappings

Rais Ahmad and Mohd Dilshad

Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

Received 18 December 2010; Accepted 23 December 2010

Academic Editor: Qamrul Hasan Ansari

Copyright © 2011 Rais Ahmad and Mohd Dilshad. 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.

Abstract

We study variational-like inclusions involving infinite family of set-valued mappings and their equivalence with resolvent equations. It is established that variational-like inclusions in real Banach spaces are equivalent to fixed point problems. This equivalence is used to suggest an iterative algorithm for solving resolvent equations. Some examples are constructed.