Abstract and Applied Analysis
Volume 2013 (2013), Article ID 232170, 7 pages
http://dx.doi.org/10.1155/2013/232170
Research Article

Proximal Point Algorithms for Finding a Zero of a Finite Sum of Monotone Mappings in Banach Spaces

H. Zegeye1 and N. Shahzad2

1Departement of Mathematics, University of Botswana, Private Bag 00704, Gaborone, Botswana
2Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 15 February 2013; Revised 30 March 2013; Accepted 31 March 2013

Academic Editor: Yisheng Song

Copyright © 2013 H. Zegeye and N. Shahzad. 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 introduce an iterative process which converges strongly to a zero of a finite sum of monotone mappings under certain conditions. Applications to a convex minimization problem are included. Our theorems improve and unify most of the results that have been proved in this direction for this important class of nonlinear mappings.