Strong Convergence of New Two-Step Viscosity Iterative Approximation Methods for Set-Valued Nonexpansive Mappings in CAT(0) Spaces. (2nd July 2018)

• Record Type: Journal Article
• Authors: Xiong, Ting-jian; Lan, Heng-you
• Other Names: Gopal Dhananjay Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2018(2018)
• Publication Date: 2018-07-02
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2018/1280241
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : This paper is for the purpose of introducing and studying a class of new two-step viscosity iteration approximation methods for finding fixed points of set-valued nonexpansive mappings inC A T ( 0 ) spaces. By means of some properties and characteristic toC A T ( 0 ) space and using Cauchy-Schwarz inequality and Xu's inequality, strong convergence theorems of the new two-step viscosity iterative process for set-valued nonexpansive and contraction operators in completeC A T ( 0 ) spaces are provided. The results of this paper improve and extend the corresponding main theorems in the literature.