Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 756492, 22 pages
Research Article

Strong Convergence for Mixed Equilibrium Problems of Infinitely Nonexpansive Mappings

Division of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand

Received 29 March 2010; Accepted 24 May 2010

Academic Editor: Tomonari Suzuki

Copyright © 2010 Jintana Joomwong. 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 introduce a new iterative scheme for finding a common element of infinitely nonexpansive mappings, the set of solutions of a mixed equilibrium problems, and the set of solutions of the variational inequality for an α-inverse-strongly monotone mapping in a Hilbert Space. Then, the strong converge theorem is proved under some parameter controlling conditions. The results of this paper extend and improve the results of Jing Zhao and Songnian He(2009) and many others. Using this theorem, we obtain some interesting corollaries.