A New Iterative Method for Equilibrium Problems and Fixed Point Problems. (31st December 2013)

• Record Type: Journal Article
• Authors: Latif, Abdul; Eslamian, Mohammad
• Other Names: Ćirić Ljubomir B. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-12-31
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/178053
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : Introducing a new iterative method, we study the existence of a common element of the set of solutions of equilibrium problems for a family of monotone, Lipschitz-type continuous mappings and the sets of fixed points of two nonexpansive semigroups in a real Hilbert space. We establish strong convergence theorems of the new iterative method for the solution of the variational inequality problem which is the optimality condition for the minimization problem. Our results improve and generalize the corresponding recent results of Anh (2012), Cianciaruso et al. (2010), and many others.