Discontinuity at fixed point and metric completeness

Ravindra K. Bisht, Vladimir Rakocevic

Abstract

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.


Keywords

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

Subject classification

47H09; 47H10

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References

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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



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