Viscosity Approximation Method for System of Variational Inclusions Problems and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings. (13th May 2012)

• Record Type: Journal Article
• Authors: Jaiboon, Chaichana; Kumam, Poom
• Other Names: Yao Yonghong Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2012(2012)
• Publication Date: 2012-05-13
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2012/816529
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : We propose new iterative schemes for finding the common element of the set of common fixed points of countable family of nonexpansive mappings, the set of solutions of the variational inequality problem for relaxed cocoercive and Lipschitz continuous, the set of solutions of system of variational inclusions problem, and the set of solutions of equilibrium problems in a real Hilbert space by using the viscosity approximation method. We prove strong convergence theorem under some parameters. The results in this paper unify and generalize some well-known results in the literature.