Mixed iterative algorithms for the multiple-set split equality common fixed-point problems without prior knowledge of operator norms. (3rd May 2016)

• Record Type: Journal Article
• Authors: Zhao, Jing; Wang, Shengnan
• Is Part Of: Optimization. Volume 65:Number 5(2016)
• Page Start: 1069
• Page End: 1083
• Publication Date: 2016-05-03
• Subjects: the multiple-set split equality common fixed-point problem -- quasi-nonexpansive mapping -- weak convergence -- iterative algorithms -- Hilbert space; 47H09 -- 47H10 -- 47J05 -- 54H25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2015.1072716
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : Let, , be real Hilbert spaces, let, be two bounded linear operators. The multiple-set split equality common fixed-point problem (MSECFP) under consideration in this paper is to (Section.Display) where are integers, and are quasi-nonexpansive mappings with nonempty fixed-point sets. Note that, the above problem (1) allows asymmetric and partial relations between the variables and . If and, then the MSECFP (1) reduces to the multiple-set split common fixed-point problem proposed by Censor et al. In this paper, we introduce mixed cyclic and simultaneous iterative algorithms for the MSECFP (1). We introduce a way of selecting the stepsizes such that the implementation of our algorithms does not need any prior information about the operator norms. Weak convergence results are given.