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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