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New discontinuity results at fixed point on metric spaces

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Abstract

Recently, the discontinuity problem at a fixed point has been studied by various aspects. In this paper, we investigate new solutions to the discontinuity problem using appropriate contractive conditions which are strong enough to generate fixed points (resp. common fixed points) but which do not force the map (resp. maps) to be continuous at fixed points. An application is also given to the fixed-circle problem on a metric space.

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Acknowledgements

The authors would like to thank the referees for their positive and insightful comments on the manuscript. This work is supported by the Scientific Research Projects Unit of Balıkesir University under the project number 2020/019.

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  1. Department of Mathematics, Balıkesir University, 10145, Balıkesir, Turkey

    Nihal Özgür & Nihal Taş

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  1. Nihal Özgür
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  2. Nihal Taş
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Correspondence to Nihal Özgür.

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Özgür, N., Taş, N. New discontinuity results at fixed point on metric spaces. J. Fixed Point Theory Appl. 23, 28 (2021). https://doi.org/10.1007/s11784-021-00863-3

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