Parallel Iterative Methods for Solving the Split Common Fixed Point Problem in Hilbert Spaces. (18th May 2020)

• Record Type: Journal Article
• Authors: Reich, Simeon; Tuyen, Truong Minh; Trang, Nguyen Minh
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 7(2020)
• Page Start: 778
• Page End: 805
• Publication Date: 2020-05-18
• Subjects: Metric projection -- nonexpansive mapping -- parallel algorithm -- split common fixed point problem; 47H05 -- 47H09 -- 49J53 -- 90C25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1681000
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: We introduce three new parallel algorithms for solving the split common fixed point problem in Hilbert spaces. Those iterative methods for solving split common fixed point problems which involve step sizes that depend on the norm of a given bounded linear operator are often not easy to implement because one has to compute the norm of this operator. Therefore, in addition to two such algorithms, we also propose a new iterative method involving step sizes which are selected in such a way that the implementation of the method does not require the computation or estimation of the norm of the given operator. Several corollaries of our main results regarding the solution of multiple-set split feasibility, split common null point, split variational inequality and split mixed equilibrium problems are also presented.