Annals of Functional Analysis

Equivalent results to Banach’s contraction principle

Maher Berzig, Cristina-Olimpia Rus, and Mircea-Dan Rus

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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.

Article information

Ann. Funct. Anal. Volume 8, Number 4 (2017), 435-445.

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

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Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]
Secondary: 03E20: Other classical set theory (including functions, relations, and set algebra) 54E35: Metric spaces, metrizability 54E99: None of the above, but in this section 54H25: Fixed-point and coincidence theorems [See also 47H10, 55M20]

fixed point binary relation extended metric contraction principle equivalent theorems


Berzig, Maher; Rus, Cristina-Olimpia; Rus, Mircea-Dan. Equivalent results to Banach’s contraction principle. Ann. Funct. Anal. 8 (2017), no. 4, 435--445. doi:10.1215/20088752-2017-0008.

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