A New Approximation Scheme Combining the Viscosity Method with Extragradient Method for Mixed Equilibrium Problems. (12th January 2010)

• Record Type: Journal Article
• Authors: Peng, Jian-Wen; Wu, Soon-Yi
• Other Names: Reich Simeon Academic Editor.
• Is Part Of: Fixed point theory and applications. Volume 2009(2009)
• Publication Date: 2010-01-12
• Subjects: Fixed point theory -- Periodicals; Mappings (Mathematics) -- Periodicals; 515.7248
• DOI: 10.1155/2009/257089
• Languages: English
• ISSNs: 1687-1812

Abstract

Abstract : We introduce a new approximation scheme combining the viscosity method with extragradient method for finding a common element of the set of solutions of a mixed equilibrium problem and the set of fixed points of a finite family of nonexpansive mappings and the set of the variational inequality for a monotone, Lipschitz continuous mapping. We obtain a strong convergence theorem for the sequences generated by these processes in Hilbert spaces. Based on this result, we also get some new and interesting results. The results in this paper generalize, extend, and improve some well-known results in the literature.