Some asymptotic stationary point theorems in topological spaces
type: Item
instance of: scholarly article
title: Some asymptotic stationary point theorems in topological spaces
zbMATH Open document ID: 1254.54053
published in: Topology and its Applications
publication date: 2012-10-11T00:00:00Z
review text: \textit{E. Tarafdar} and \textit{X.-Z. Yuan} introduced in [Appl. Math. Lett. 8, No. 6, 79--81 (1995; Zbl 0837.54011)] the notion of topological contraction and proved that every upper semicontinuous set-valued topological contraction with closed values on a compact topological space has a unique stationary point. In the paper under review, an asymptotic version of this result is derived and extended by relaxing compactness of the space. It is shown that any generalized sequence of iterations with an arbitrary initial point of a set-valued map on a complete first countable Hausdorff uniform space converges to its stationary point. Examples are given to distinguish these results from some known ones.
reviewed by: Zoran Kadelburg
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 47H08
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 6092991
zbMATH Keywords: stationary point
zbMATH Keywords: topological contraction
zbMATH Keywords: measure of noncompactness
zbMATH Keywords: generalized \(\mu\)-set contraction
author: M. Fakhar
author: Z. Soltani
author: Jafar Zafarani
MaRDI profile type: Publication
full work available at URL: j.topol.2012.08.007
OpenAlex ID: W2023185931
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DOI: 10.1016/J.TOPOL.2012.08.007
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description: scientific article; zbMATH DE number 6092991