Copyright © 2012 Pongsakorn Sunthrayuth and Poom Kumam. 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.

Abstract

We introduce a new general system of generalized nonlinear mixed composite-type equilibria and propose a new iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a general system of generalized nonlinear mixed composite-type equilibria, and the set of fixed points of a countable family of strict pseudocontraction mappings. Furthermore, we prove the strong convergence theorem of the purposed iterative scheme in a real Hilbert space. As applications, we apply our results to solve a certain minimization problem related to a strongly positive bounded linear operator. Finally, we also give a numerical example which supports our results. The results obtained in this paper extend the recent ones announced by many others.