Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 794178, 21 pages
doi:10.1155/2009/794178
An iterative algorithm combining viscosity method with parallel method for a generalized equilibrium problem and strict pseudocontractions
Jian-Wen Peng1
, Yeong-Cheng Liou2
and Jen-Chih Yao3
1College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China
2Department of Information Management, Cheng Shiu University, Kaohsiung, Taiwan 833, Taiwan
3Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 804, Taiwan
Abstract
We introduce a new approximation scheme combining the viscosity method with parallel method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a family of finitely strict pseudocontractions. We obtain a strong convergence theorem for the sequences generated by these processes in Hilbert spaces. Based on this result, we also get some new and interesting results. The results in this paper extend and improve some well-known results in the literature.