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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 451279, 9 pages
http://dx.doi.org/10.1155/2014/451279
Research Article

Iterative Schemes for Finite Families of Maximal Monotone Operators Based on Resolvents

School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China

Received 25 January 2014; Accepted 12 March 2014; Published 14 April 2014

Academic Editor: Jinlu Li

Copyright © 2014 Li Wei and Ruilin Tan. 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

The purpose of this paper is to present two iterative schemes based on the relative resolvent and the generalized resolvent, respectively. And, it is shown that the iterative schemes converge weakly to common solutions for two finite families of maximal monotone operators in a real smooth and uniformly convex Banach space and one example is demonstrated to explain that some assumptions in the main results are meaningful, which extend the corresponding works by some authors.