Abstract and Applied Analysis
Volume 2012 (2012), Article ID 414718, 26 pages
Research Article

A New General System of Generalized Nonlinear Mixed Composite-Type Equilibria and Fixed Point Problems with an Application to Minimization Problems

Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bang Mod, Bangkok 10140, Thailand

Received 9 August 2012; Accepted 24 September 2012

Academic Editor: RuDong Chen

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.


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.