Several iterative algorithms for solving the split common fixed point problem of directed operators with applications. (2nd January 2016)

• Record Type: Journal Article
• Authors: Tang, Yu-Chao; Liu, Li-Wei
• Is Part Of: Optimization. Volume 65:Number 1(2016)
• Page Start: 53
• Page End: 65
• Publication Date: 2016-01-02
• Subjects: split common fixed point problem -- directed operators -- simultaneous; 47J25 -- 47N10 -- 65J15 -- 90C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2014.984708
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we propose a new simultaneous iterative algorithm for solving the split common fixed point problem of directed operators. Inspired by the idea of cyclic iterative algorithm, we also introduce two iterative algorithms which combine the process of cyclic and simultaneous together. Under mild assumptions, we prove convergence of the proposed iterative sequences. As applications, we obtain several iteration schemes to solve the inverse problem of multiple-sets split feasibility problem. Numerical experiments are presented to confirm the efficiency of the proposed iterative algorithms.