Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 350979, 20 pages
Research Article

A New Hybrid Algorithm for Variational Inclusions, Generalized Equilibrium Problems, and a Finite Family of Quasi-Nonexpansive Mappings

Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Received 12 June 2009; Accepted 28 September 2009

Academic Editor: Naseer Shahzad

Copyright © 2009 Prasit Cholamjiak and Suthep Suantai. 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.


We proposed in this paper a new iterative scheme for finding common elements of the set of fixed points of a finite family of quasi-nonexpansive mappings, the set of solutions of variational inclusion, and the set of solutions of generalized equilibrium problems. Some strong convergence results were derived by using the concept of W-mappings for a finite family of quasi-nonexpansive mappings. Strong convergence results are derived under suitable conditions in Hilbert spaces.