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Relation-theoretic metrical fixed-point results via \(\varvec{w}\)-distance with applications

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A Correction to this article was published on 27 July 2018

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Abstract

In this article, utilizing the concept of w-distance, we prove the celebrated Banach’s fixed-point theorem in metric spaces equipped with an arbitrary binary relation. Necessarily, our findings unveil another direction of relation-theoretic metrical fixed-point theory. In addition, our paper consists of several non-trivial examples which signify the motivation of such investigations. Finally, our obtained results enable us to explore the existence of solutions of nonlinear fractional differential equations and fractional thermostat model involving the Caputo fractional derivative.

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Change history

  • 27 July 2018

    The Example 2.3 in [3] contains an inaccuracy as the mapping T considered here is not a self-mapping.

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Acknowledgements

The authors’ thanks are due to anonymous referee for his/her valuable and insightful comments, ideas which literally helped to improve the depth of the article. Also, the authors are thankful to Ankush Chanda for his help during the revision of the manuscript. The first named author would like to express her sincere gratitude to DST-INSPIRE, New Delhi, India for their financial supports under INSPIRE fellowship scheme.

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  1. Department of Mathematics, National Institute of Technology Durgapur, Durgapur, West Bengal, India

    Tanusri Senapati & Lakshmi Kanta Dey

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  1. Tanusri Senapati
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  2. Lakshmi Kanta Dey
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Correspondence to Lakshmi Kanta Dey.

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Senapati, T., Dey, L.K. Relation-theoretic metrical fixed-point results via \(\varvec{w}\)-distance with applications. J. Fixed Point Theory Appl. 19, 2945–2961 (2017). https://doi.org/10.1007/s11784-017-0462-9

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