Journal of Applied Mathematics
Volume 2012 (2012), Article ID 416476, 23 pages
http://dx.doi.org/10.1155/2012/416476
Research Article

Convergence Theorems for Equilibrium Problems and Fixed-Point Problems of an Infinite Family of 𝑘 𝑖 -Strictly Pseudocontractive Mapping in Hilbert Spaces

Haitao Che,1,2 Meixia Li,1 and Xintian Pan1

1School of Mathematics and Information Science, Weifang University, Shandong Weifang 261061, China
2School of Management Science, Qufu Normal University, Shandong Rizhao 276800, China

Received 28 February 2012; Revised 8 June 2012; Accepted 24 June 2012

Academic Editor: Jong Hae Kim

Copyright © 2012 Haitao Che 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 first extend the definition of Wn from an infinite family of nonexpansive mappings to an infinite family of strictly pseudocontractive mappings, and then propose an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of an infinite family of 𝑘 𝑖 -strictly pseudocontractive mappings in Hilbert spaces. The results obtained in this paper extend and improve the recent ones announced by many others. Furthermore, a numerical example is presented to illustrate the effectiveness of the proposed scheme.