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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 643602, 7 pages
http://dx.doi.org/10.1155/2013/643602
Research Article

Iterative Methods for Pseudocontractive Mappings in Banach Spaces

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

Received 12 February 2013; Accepted 3 March 2013

Academic Editor: Yisheng Song

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 a reflexive Banach space having a uniformly Gâteaux differentiable norm. Let be a nonempty closed convex subset of , a continuous pseudocontractive mapping with , and a continuous bounded strongly pseudocontractive mapping with a pseudocontractive constant . Let and be sequences in satisfying suitable conditions and for arbitrary initial value , let the sequence be generated by If either every weakly compact convex subset of has the fixed point property for nonexpansive mappings or is strictly convex, then converges strongly to a fixed point of , which solves a certain variational inequality related to .