Copyright © 2012 Nopparat Wairojjana and Poom Kumam. 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

This paper deals with new methods for approximating a solution to the fixed point problem; find , where is a Hilbert space, is a closed convex subset of , is a -contraction from into , , is a strongly positive linear-bounded operator with coefficient , , is a nonexpansive mapping on and denotes the metric projection on the set of fixed point of . Under a suitable different parameter, we obtain strong convergence theorems by using the projection method which solves the variational inequality for , where . Our results generalize and improve the corresponding results of Yao et al. (2010) and some authors. Furthermore, we give an example which supports our main theorem in the last part.