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November 2017 Equivalent results to Banach’s contraction principle
Maher Berzig, Cristina-Olimpia Rus, Mircea-Dan Rus
Ann. Funct. Anal. 8(4): 435-445 (November 2017). DOI: 10.1215/20088752-2017-0008

Abstract

We present two versions of the well-known Banach contraction principle: one in the context of extended metric spaces for which the distance mapping is allowed to be infinite, the other in the context of metric spaces endowed with a compatible binary relation. We also point out that these two results and the Banach contraction principle are actually equivalent.

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Maher Berzig. Cristina-Olimpia Rus. Mircea-Dan Rus. "Equivalent results to Banach’s contraction principle." Ann. Funct. Anal. 8 (4) 435 - 445, November 2017. https://doi.org/10.1215/20088752-2017-0008

Information

Received: 6 February 2016; Accepted: 21 November 2016; Published: November 2017
First available in Project Euclid: 23 May 2017

zbMATH: 06841325
MathSciNet: MR3717166
Digital Object Identifier: 10.1215/20088752-2017-0008

Subjects:
Primary: 47H10
Secondary: 03E20 , 54E35 , 54E99 , 54H25

Keywords: binary relation , contraction principle , equivalent theorems , extended metric , fixed point

Rights: Copyright © 2017 Tusi Mathematical Research Group

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Vol.8 • No. 4 • November 2017
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