Discontinuity at fixed point and metric completeness

Ravindra K. Bisht, Vladimir Rakocevic


In this paper, we prove some new fixed point theorems for a generalized class of Meir-Keeler type mappings, which give some new solutions to the Rhoades open problem regarding the existence of contractive mappings that admit discontinuity at the fixed point. In addition to it, we prove that our theorems characterize completeness of the metric space as well as Cantor's intersection property.


fixed point; completeness; discontinuity; Cantor's intersection property

Subject classification

47H09; 47H10

Full Text:



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1. On a probabilistic version of Meir-Keeler type fixed point theorem for a family of discontinuous operators
Ravindra K. Bisht, Vladimir Rakocević
Applied General Topology  vol: 22  issue: 2  first page: 435  year: 2021  
doi: 10.4995/agt.2021.15561

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

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