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 .