Strong and \(\Delta\)-convergence theorems for common fixed points of a finite family of multivalued demicontractive mappings in CAT\((0)\) spaces
type: Item
instance of: scholarly article
title: Strong and \(\Delta\)-convergence theorems for common fixed points of a finite family of multivalued demicontractive mappings in CAT\((0)\) spaces
zbMATH Open document ID: 1469.65099
DOI: 10.1155/2014/805168
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Let \(K\) be a nonempty closed and convex subset of a complete CAT(0) space. Let \(T_i : K \rightarrow \text{C} \text{B} \left(K\right)\), \(i = 1,2, \dots, m\), be a family of multivalued demicontractive mappings such that \(F : = \bigcap_{i = 1}^m F(T_i) \neq \varnothing\). A~Krasnoselskii-type iterative sequence is shown to \(\Delta\)-converge to a common fixed point of the family \(\left\{T_i, i = 1,2, \dots, m\right\}\). Strong convergence theorems are also proved under some additional conditions. Our theorems complement and extend several recent important results on approximation of fixed points of certain nonlinear mappings in CAT\((0)\) spaces. Furthermore, our method of the proof is of special interest.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54E40
zbMATH DE Number: 7023110
author: C. E. Chidume
author: Abdulmalik Usman Bello
author: Patrice Ndambomve
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/805168
OpenAlex ID: W2060842854
Wikidata QID: Q59041653
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description: scientific article; zbMATH DE number 7023110