Strong Convergence of a Split Common Fixed Point Problem. (2nd October 2016)

• Record Type: Journal Article
• Authors: Eslamian, Mohammad; Eslamian, Peyman
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 10(2016)
• Page Start: 1248
• Page End: 1266
• Publication Date: 2016-10-02
• Subjects: Quasi-nonexpansive mapping -- split common fixed point problems -- split variational inequality problem -- strong convergence; 49J53 -- 65K10 -- 49M37 -- 90C25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1200076
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we present a new general algorithm for solving the split common fixed point problem in an infinite dimensional Hilbert space, which is to find a point which belongs to the common fixed point of a family of quasi-nonexpansive mappings such that its image under a linear transformation belongs to the common fixed point of another family of quasi-nonexpansive mappings in the image space. We establish the strong convergence for the algorithm to find a unique solution of the variational inequality, which is the optimality condition for the minimization problem. The algorithm and its convergence results improve and develop previous results in this field.