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

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 in CAT(0) spaces. By means of some properties and characteristic to CAT(0) space and using Cauchy-Schwarz inequalit...

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Bibliographic Details
Published inJournal of function spaces Vol. 2018; no. 2018; pp. 1 - 8
Main Authors Xiong, Ting-jian, Lan, Heng-you
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 01.01.2018
Hindawi
John Wiley & Sons, Inc
Hindawi Limited
Subjects
Analysis
Applied mathematics
Approximation
Contraction
Convergence
Game theory
Geometry
Mathematical analysis
Mathematical optimization
Methods
Theorems
Viscosity
Japan
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Summary: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 in CAT(0) spaces. By means of some properties and characteristic to CAT(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 complete CAT(0) spaces are provided. The results of this paper improve and extend the corresponding main theorems in the literature.
ISSN:2314-8896
2314-8888
DOI:10.1155/2018/1280241