Stable iteration procedures in metric spaces which generalize a Picard-type iteration
type: Item
instance of: scholarly article
title: Stable iteration procedures in metric spaces which generalize a Picard-type iteration
zbMATH Open document ID: 1203.54039
DOI: 10.1155/2010/953091
published in: Fixed Point Theory and Applications
publication date: 2010-09-28T00:00:00Z
full work available at URL: https://eudml.org/doc/223848
review text: Let \((X,d)\) be a complete metric space and \(f, T\) be self-mappings of \(X\). The Picard iteration \(x_{k+1}=f(Tx_k)\) is said to be \(T\)-stable if for any \(x_0\in X\) the sequence \(\{x_k\}\) converges to a fixed point of \(fT\), whenever \(\lim_{k\rightarrow \infty}d(x_{k+1}, Tx_k)=0\). By using the concepts of altering-distance function and extended altering-distance function, the author obtains generalizations of some results concerning the \(T\)-stability of the iterations.
reviewed by: Mircea Balaj
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 5792465
zbMATH Keywords: fixed point
zbMATH Keywords: Picard iteration
zbMATH Keywords: altering-distance function
zbMATH Keywords: extended altering-distance function
Wikidata QID: Q57675288
author: M. De la Sen
MaRDI profile type: Publication
OpenAlex ID: W2165026984
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description: scientific article; zbMATH DE number 5792465