Iterative methods for the split feasibility problem and the fixed point problem in Banach spaces. (4th May 2019)

• Record Type: Journal Article
• Authors: Suantai, Suthep; Witthayarat, Uamporn; Shehu, Yekini; Cholamjiak, Prasit
• Is Part Of: Optimization. Volume 68:Number 5(2019)
• Page Start: 955
• Page End: 980
• Publication Date: 2019-05-04
• Subjects: Split feasibility problem -- weak and strong convergence -- self-adaptive method -- fixed point problem -- Banach space; 47H04 -- 47H10 -- 54H25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1566328
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this work, we suggest modifications of the self-adaptive method for solving the split feasibility problem and the fixed point problem of nonexpansive mappings in the framework of Banach spaces. Without the assumption on the norm of the operator, we prove that the sequences generated by our algorithms weakly and strongly converge to a solution of the problems. The numerical experiments are demonstrated to show the efficiency and the implementation of our algorithms.