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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 369412, 7 pages
http://dx.doi.org/10.1155/2013/369412
Research Article

Convergence of a Viscosity Iterative Method for Multivalued Nonself-Mappings in Banach Spaces

Department of Mathematics, Dong-A University, Busan 604-714, Republic of Korea

Received 9 October 2012; Accepted 9 January 2013

Academic Editor: Yuriy Rogovchenko

Copyright © 2013 Jong Soo Jung. 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

Let be a reflexive Banach space having a weakly sequentially continuous duality mapping with gauge function , a nonempty closed convex subset of , and a multivalued nonself-mapping such that is nonexpansive, where . Let be a contraction with constant . Suppose that, for each and , the contraction defined by has a fixed point . Let , and be three sequences in satisfying approximate conditions. Then, for arbitrary , the sequence generated by for all converges strongly to a fixed point of .