Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 617248, 12 pages
Strong Convergence Theorem by Monotone Hybrid Algorithm for Equilibrium Problems, Hemirelatively Nonexpansive Mappings, and Maximal Monotone Operators
College of Science, Civil Aviation University of China, Tianjin 300300, China
Received 17 June 2008; Accepted 11 November 2008
Academic Editor: Wataru Takahashi
Copyright © 2008 Yun Cheng and Ming Tian. 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 hybrid iterative algorithm for finding a common
element of the set of fixed points of hemirelatively nonexpansive mappings
and the set of solutions of an equilibrium problem and for finding a common
element of the set of zero points of maximal monotone operators and the
set of solutions of an equilibrium problem in a Banach space. Using this
theorem, we obtain three new results for finding a solution of an equilibrium
problem, a fixed point of a hemirelatively nonexpnasive mapping, and a zero
point of maximal monotone operators in a Banach space.