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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 892980, 12 pages
http://dx.doi.org/10.1155/2012/892980
Research Article

A Proximal Point Method Involving Two Resolvent Operators

Department of Applied Sciences, Botswana International University of Science and Technology, Private Bag 41, Gaborone, Botswana

Received 29 May 2012; Accepted 1 August 2012

Academic Editor: Svatoslav Staněk

Copyright © 2012 Oganeditse A. Boikanyo. 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 construct a sequence of proximal iterates that converges strongly (under minimal assumptions) to a common zero of two maximal monotone operators in a Hilbert space. The algorithm introduced in this paper puts together several proximal point algorithms under one frame work. Therefore, the results presented here generalize and improve many results related to the proximal point algorithm which were announced recently in the literature.