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arXiv · 2502.02595

Three point analogue of \'Ciri\'c-Reich-Rus type mappings with non-unique fixed points

Ravindra K. Bisht·Evgeniy Petrov
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Abstract

In this paper, we introduce a three-point analogue of \'Ciri\'c-Reich-Rus type mappings, termed as generalized \'Ciri\'c-Reich-Rus type mappings. We demonstrate that these mappings generally exhibit discontinuity within their domain of definition but necessitate continuity at their fixed points. We showcase the existence and non-uniqueness of fixed points for these generalized \'Ciri\'c-Reich-Rus type mappings. By imposing additional conditions, specifically asymptotic regularity and continuity, we extend the applicability of fixed-point theorems to a broader class of mappings. Finally, we obtain two fixed point theorems for generalized \'Ciri\'c-Reich-Rus type mappings in metric spaces that are not necessarily complete.

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Ravindra K. Bisht, Evgeniy Petrov. 2024-12-31. Three point analogue of \'Ciri\'c-Reich-Rus type mappings with non-unique fixed points. https://doi.org/10.1007/s41478-024-00743-2

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