On best proximity pair theorems and fixed-point theorems
type: Item
instance of: scholarly article
title: On best proximity pair theorems and fixed-point theorems
zbMATH Open document ID: 1023.47035
DOI: 10.1155/S1085337503209064
author: P. S. Srinivasan
author: P. Veeramani
published in: Abstract and Applied Analysis
publication date: 2003-03-17T00:00:00Z
full work available at URL: https://eudml.org/doc/50383
review text: Summary: The significance of fixed-point theory stems from the fact that it furnishes a unified approach and constitutes an important tool in solving equations which are not necessarily linear. On the other hand, if the fixed-point equation \(Tx=x\) does not possess a solution, it is contemplated to resolve a problem of finding an element \(x\) such that \(x\) is in proximity to \(Tx\) in some sense. Best proximity pair theorems analyze the conditions under which the optimization problem, namely \(\min_{x\in A}d(x,Tx)\) has a solution. In this paper, we discuss the difference between best approximation theorems and best proximity pair theorems. We also discuss an application of a best proximity pair theorem to the theory of games.
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 91A06
zbMATH DE Number: 1883733
zbMATH Keywords: multivalued map between metric spaces
zbMATH Keywords: best proximity pair
zbMATH Keywords: best approximation
zbMATH Keywords: game theory
MaRDI profile type: Publication
OpenAlex ID: W2040243673
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description: scientific article; zbMATH DE number 1883733