The Split Equality Fixed Point Problem for Quasi-Pseudo-Contractive Mappings Without Prior Knowledge of Norms. (18th May 2020)

• Record Type: Journal Article
• Authors: Boikanyo, Oganeditse A.; Zegeye, Habtu
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 7(2020)
• Page Start: 759
• Page End: 777
• Publication Date: 2020-05-18
• Subjects: Demicontractive operators -- directed operators -- fixed point -- feasibility problem -- quasi nonexpansive mapping -- quasi-pseudo contractive mapping; 47H09 -- 47H10 -- 47H20 -- 47J20 -- 65J15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1675170
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Recently, Chang et al. (2015) constructed an algorithm that converges weakly to the solution of the split equality fixed point problem for quasi-pseudo-contractive mappings under some suitable conditions. They also showed that strong convergence is obtained in the case when the quasi-pseudo-contractive mappings are semi-compact. In this article, we construct an algorithm for quasi-pseudo-contractive mappings that always converge strongly to some solution of the split equality fixed point problem under mild conditions. We mention that we do not require the quasi-pseudo-contractive mappings to be semi-compact to obtain strong convergence. The algorithm does not require any prior knowledge of operator norms. The result of this article provides a unified framework for this type of problems.