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Retracted

This article has been retracted as it is essentially identical in content with a previously published paper by the same authors titled “A New Generalized Resolvent and Application in Banach Mappings.” This manuscript was published in East Asian Mathematical Journal, Volume 30 (2014), No. 1, pp. 69–77.

View the full Retraction here.

References

  1. X. Wang, J. Chen, and H. Tong, “Iterative schemes by a new generalized resolvent for a monotone mapping and a relatively weak nonexpansive mapping,” Journal of Applied Mathematics, vol. 2014, Article ID 603186, 6 pages, 2014.
Journal of Applied Mathematics
Volume 2014, Article ID 603186, 6 pages
http://dx.doi.org/10.1155/2014/603186
Research Article

Iterative Schemes by a New Generalized Resolvent for a Monotone Mapping and a Relatively Weak Nonexpansive Mapping

College of Mathematics and Computer, Hebei University, Baoding 071002, China

Received 25 November 2013; Accepted 2 March 2014; Published 7 April 2014

Academic Editor: Abdel-Maksoud A. Soliman

Copyright © 2014 Xian Wang et al. 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 a new generalized resolvent in a Banach space and discuss some of its properties. Using these properties, we obtain an iterative scheme for finding a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping. Furthermore, strong convergence of the scheme to a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping is proved.