Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 617248, 12 pages
doi:10.1155/2008/617248

Strong convergence theorem by monotone hybrid algorithm for equilibrium problems, hemirelatively nonexpansive mappings, and maximal monotone operators

Abstract

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.