A Hybrid-Extragradient Scheme for System of Equilibrium Problems, Nonexpansive Mappings, and Monotone Mappings. (1st December 2010)

• Record Type: Journal Article
• Authors: Peng, Jian-Wen; Wu, Soon-Yi; Fan, Gang-Lun
• Other Names: Yao Jen Chih Academic Editor.
• Is Part Of: Fixed point theory and applications. Volume 2011(2011)
• Publication Date: 2010-12-01
• Subjects: Fixed point theory -- Periodicals; Mappings (Mathematics) -- Periodicals; 515.7248
• DOI: 10.1155/2011/232163
• Languages: English
• ISSNs: 1687-1812

Abstract

Abstract : We introduce a new iterative scheme based on both hybrid method and extragradient method for finding a common element of the solutions set of a system of equilibrium problems, the fixed points set of a nonexpansive mapping, and the solutions set of a variational inequality problems for a monotone andk -Lipschitz continuous mapping in a Hilbert space. Some convergence results for the iterative sequences generated by these processes are obtained. The results in this paper extend and improve some known results in the literature.