A modified Mann iterative scheme by generalized f-projection for a countable family of relatively quasi-nonexpansive mappings and a system of generalized mixed equilibrium problems

• Published in: Fixed point theory and applications (Hindawi Publishing Corporation) Vol. 2011; no. 1; p. 104
• Main Authors: Saewan, Siwaporn, Kumam, Poom
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 21.12.2011; BioMed Central Ltd
• Subjects: Analysis; Applications of Mathematics; Differential Geometry; Mathematical and Computational Biology; Mathematics; Mathematics and Statistics; Topology; maximal monotone operator; The generalized; system of generalized mixed equilibrium problems; projection operator; monotone mappings; relatively quasi-nonexpansive mapping
• ISSN: 1687-1812; 1687-1812
• DOI: 10.1186/1687-1812-2011-104

The purpose of this paper is to introduce a new hybrid projection method based on modified Mann iterative scheme by the generalized f -projection operator for a countable family of relatively quasi-nonexpansive mappings and the solutions of the system of generalized mixed equilibrium problems. Furthermore, we prove the strong convergence theorem for a countable family of relatively quasi-nonexpansive mappings in a uniformly convex and uniform smooth Banach space. Finally, we also apply our results to the problem of finding zeros of B -monotone mappings and maximal monotone operators. The results presented in this paper generalize and improve some well-known results in the literature. 2000 Mathematics Subject Classification : 47H05; 47H09; 47H10.