A New Iterative Scheme for Countable Families of Weak Relatively Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems. (12th January 2011)

• Record Type: Journal Article
• Authors: Shehu, Yekini
• Other Names: Zafer A. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2010(2010)
• Publication Date: 2011-01-12
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2010/861031
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of weak relatively nonexpansive mappings which is also a solution to a system of generalized mixed equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth using the properties of generalizedf -projection operator. Using this result, we discuss strong convergence theorem concerning generalH -monotone mappings and system of generalized mixed equilibrium problems in Banach spaces. Our results extend many known recent results in the literature.