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Fuzzy fixed point results via simulation functions

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Abstract

We inaugurate two concepts, admissible hybrid fuzzy \( {\mathcal{Z}}\)-contractions and hybrid fuzzy \( {\mathcal{Z}}\)-contractions in the bodywork of b-metric spaces and establish sufficient criteria for fuzzy fixed points for such contractions. Nontrivial illustrations are constructed to support the hypotheses of our main notions. From application point of view, a handful of fixed point results of b-metric spaces endowed with partial ordering and graph are deduced. The ideas established herein unify and complement several well-known crisp and fuzzy fixed point theorems in the framework of both single-valued and set-valued mappings involving either linear or nonlinear contractions. A few important consequences of our main theorem are highlighted and analysed by using various forms of simulation functions.

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Acknowledgements

The authors are thankful to the editors and the anonymous reviewers for their valuable suggestions and comments that helped to improve this manuscript.

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  1. Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria

    Shehu Shagari Mohammed & Ibrahim Aliyu Fulatan

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  1. Shehu Shagari Mohammed
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  2. Ibrahim Aliyu Fulatan
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Correspondence to Shehu Shagari Mohammed.

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Mohammed, S.S., Fulatan, I.A. Fuzzy fixed point results via simulation functions. Math Sci 16, 137–148 (2022). https://doi.org/10.1007/s40096-021-00405-5

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