Strong convergence theorems of an iterative scheme for strictly pseudocontractive mappings in Banach spaces. (3rd June 2018)

• Record Type: Journal Article
• Authors: Yang, Liping
• Is Part Of: Optimization. Volume 67:Number 6(2018)
• Page Start: 855
• Page End: 863
• Publication Date: 2018-06-03
• Subjects: Modified Ishikawa iterative process with errors -- strong convergence -- strictly pseudocontractive mapping -- fixed point -- demi-compact; 47H09 -- 47H10 -- 47J25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1430147
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: The article establishes the sufficient and necessary conditions for the strong convergence of the Ishikawa iterative scheme with random errors in the sense of Xu for a strictly pseudocontractive mapping in an arbitrary real Banach space under certain assumptions. It affirmatively answers the open question that put forth by Zeng. The results in this paper extend and improve the corresponding results of Browder, Petryshyn, Rhoades, Osilike and Zeng.