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Three point analogue of Ćirić-Reich-Rus type mappings with non-unique fixed points

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Abstract

In this paper, we introduce a three-point analogue of Ćirić-Reich-Rus type mappings, termed as generalized Ćirić-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 Ćirić-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 Ćirić-Reich-Rus type mappings in metric spaces that are not necessarily complete.

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Acknowledgements

This work was partially supported by a grant from the Simons Foundation (Award 1160640, Presidential Discretionary-Ukraine Support Grants, E. Petrov).

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Authors and Affiliations

  1. Department of Mathematics, National Defence Academy, Pune, Khadakwasla, India

    Ravindra K. Bisht

  2. Department of Function Theory, Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Batiuka str. 19, Slovyansk, 84116, Ukraine

    Evgeniy Petrov

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  1. Ravindra K. Bisht
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  2. Evgeniy Petrov
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Correspondence to Evgeniy Petrov.

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Communicated by Simeon Reich.

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Bisht, R.K., Petrov, E. Three point analogue of Ćirić-Reich-Rus type mappings with non-unique fixed points. J Anal (2024). https://doi.org/10.1007/s41478-024-00743-2

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