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Abstract and Applied Analysis
Volume 2016, Article ID 2371857, 10 pages
http://dx.doi.org/10.1155/2016/2371857
Research Article

The Viscosity Approximation Forward-Backward Splitting Method for Zeros of the Sum of Monotone Operators

Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Private Bag Box 16, Palapye, Botswana

Received 8 September 2015; Accepted 8 December 2015

Academic Editor: Sergei V. Pereverzyev

Copyright © 2016 Oganeditse Aaron 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 investigate the convergence analysis of the following general inexact algorithm for approximating a zero of the sum of a cocoercive operator and maximal monotone operators with : , for for given in a real Hilbert space , where , , and are sequences in with for all , denotes the error sequence, and is a contraction. The algorithm is known to converge under the following assumptions on and : (i) is bounded below away from 0 and above away from 1 and (ii) is summable in norm. In this paper, we show that these conditions can further be relaxed to, respectively, the following: (i) is bounded below away from 0 and above away from 3/2 and (ii) is square summable in norm; and we still obtain strong convergence results.