A New General System of Generalized Nonlinear Mixed Composite-Type Equilibria and Fixed Point Problems with an Application to Minimization Problems. (14th November 2012)

• Record Type: Journal Article
• Authors: Sunthrayuth, Pongsakorn; Kumam, Poom
• Other Names: Chen RuDong Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-11-14
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/414718
• Languages: English
• ISSNs: 1085-3375

Abstract

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.