Convergence analysis of an iterative algorithm for fixed point problems and split feasibility problems in certain Banach spaces. (1st February 2016)

• Record Type: Journal Article
• Authors: Shehu, Y.; Ogbuisi, F.U.; Iyiola, O.S.
• Is Part Of: Optimization. Volume 65:Number 2(2016)
• Page Start: 299
• Page End: 323
• Publication Date: 2016-02-01
• Subjects: strong convergence -- split feasibility problem -- uniformly convex -- uniformly smooth -- fixed point problem -- right Bregman strongly nonexpansive mappings; 49J53 -- 65K10 -- 49M37 -- 90C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2015.1039533
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we introduce an iterative scheme for approximating a common element of the set of fixed points of left Bregman strongly nonexpansive mapping and the set of solutions of split feasibility problem. We further obtain a strong convergence result for finding a common solution of fixed point problem for left Bregman strongly nonexpansive mappings and split feasibility problem in the framework of -uniformly convex Banach spaces which are also uniformly smooth. We give an application of our result to approximating a solution of convexly constrained linear inverse problem which is also a fixed point of a left Bregman strongly nonexpansive mapping in -uniformly convex Banach spaces, which are also uniformly smooth. Finally, we give some numerical example of our result to study its efficiency and implementation. Our results complement many known related results in the literature.