Department of Mathematics, Statistics and Computer, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani 34190, Thailand
Copyright © 2011 Weerayuth Nilsrakoo. 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 sequence for finding a
common element of the set of fixed points of a relatively nonexpansive mapping
and the set of solutions of an equilibrium problem in a Banach space. Then, we
study the strong convergence of the sequences. With an appropriate setting, we
obtain the corresponding results due to Takahashi-Takahashi and Takahashi-Zembayashi. Some of our results are established with weaker assumptions.