Fixed point theorems for some discontinuous operators
type: Item
instance of: scholarly article
title: Fixed point theorems for some discontinuous operators
zbMATH Open document ID: 0549.47028
author: Lucimar Nova G.
published in: Pacific Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Let K be a closed subset of a Banach space X and \(T:K\to K\) be a not necessarily continuous map satisfying the condition \(\| Tx-Ty\|\leq a\| x-y\| +b\{\| x-Tx\| +\| y-Ty\|\}\) for all x,\(y\in K\), where \(0\leq a,b<1\). These operators are refered as belonging to the class \(D(a,b).\) The existence and uniqueness of fixed points for such operators is established. This generalizes results of Kirk, Goebel, Shimi, Hardy and Rogers et al., who assume X to be uniformly convex, T continuous and \(a+2b\leq 1\). Some applications to differential and integral operators are also considered.
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 3876029
zbMATH Keywords: existence and uniqueness of fixed points
MaRDI profile type: Publication
full work available at URL: pjm.1986.123.189
OpenAlex ID: W2125518666
DOI: 10.2140/PJM.1986.123.189
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description: scientific article; zbMATH DE number 3876029