Convergence of Inexact Mann Iterations Generated by Nearly Nonexpansive Sequences and Applications. (2nd October 2016)

• Record Type: Journal Article
• Authors: Sahu, D. R.; Ansari, Q. H.; Yao, J. C.
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 10(2016)
• Page Start: 1312
• Page End: 1338
• Publication Date: 2016-10-02
• Subjects: Accretive operator -- Mann iteration method -- nearly Lipschitzian mapping -- nonexpansive mapping -- resolvent operator -- split feasibility problem; 47H09 -- 47H10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1206566
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: The Mann iterates behave well for nonexpansive mappings for any initial guess in the domain. Our aim in this article is to extend this method to a broad class of inexact fixed point algorithms generated by nearly nonexpansive sequences in Banach spaces and to locate the weak limit of the iterates by its initial guesses. Due to the inexactness, our algorithms become efficiently applicable for a wider class of problems. As applications, we give convergence theorems for finding solutions of variational inclusion problems and constrained multiple-sets split feasibility problems. Our results are significant refinements and improvements of the corresponding results in the literature.