Convergence of infinite family of multivalued quasi-nonexpansive mappings using multistep iterative processes
type: Item
instance of: scholarly article
title: Convergence of infinite family of multivalued quasi-nonexpansive mappings using multistep iterative processes
zbMATH Open document ID: 1473.47033
DOI: 10.1155/2014/781704
author: Renu Chugh
author: Sanjay Kumar
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We prove strong and weak convergence results using multistep iterative sequences for countable family of multivalued quasi-nonexpansive mappings by using some conditions in uniformly convex real Banach space. The results presented extended and improved the corresponding result of \textit{F. Zhang} et al. [J. Appl. Math. 2013, Article ID 649537, 7 p. (2013; Zbl 1266.47101)], \textit{A. Bunyawat} and \textit{S. Suantai} [Abstr. Appl. Anal. 2012, Article ID 435790, 6 p. (2012; Zbl 1237.47068)], and some others from finite family, one countable family, and two countable families to \(k\)-number of countable families of multivalued quasi-nonexpansive mappings. Also we use a numerical example in \texttt{C++} computational programs to prove that the iterative scheme we used has better rate of convergence than other existing iterative schemes.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 7023054
zbMATH Keywords: strong convergence
zbMATH Keywords: multistep iterative sequences
zbMATH Keywords: uniformly convex real Banach space
Wikidata QID: Q59041398
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/781704
OpenAlex ID: W2110700773
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description: scientific article; zbMATH DE number 7023054