Strong Convergence Theorems for the Generalized Viscosity Implicit Rules of Asymptotically Nonexpansive Mappings in the Intermediate Sense in Hilbert Spaces. (3rd October 2018)

• Record Type: Journal Article
• Authors: Yan, Qian; Cai, Gang
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 13(2018)
• Page Start: 1351
• Page End: 1373
• Publication Date: 2018-10-03
• Subjects: Asymptotically nonexpansive mapping in the intermediate sense -- fixed point -- generalized implicit rule -- Hilbert spaces; 49H09 -- 47H10 -- 47H17 -- 49M05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1478852
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The aim of this paper is to introduce the generalized viscosity implicit rules of one asymptotically nonexpansive mapping in the intermediate sense in Hilbert spaces. We obtain some strong convergence theorems under certain assumptions imposed on the parameters. We also give a numerical example to support our main results. The results obtained in this paper improve and extend many recent ones in this culture.