Best proximity results for cyclic α-implicit contractions in quasi-metric spaces and its consequences

Poom Kumam, Surajit Karmakar, Lakshmi Kanta Dey, Ankush Chanda

Abstract


Beforehand we set up the new concept of cyclic α-implicit contractions and subsequently find best proximity points for such type of mappings on quasi-metric spaces and partially ordered quasi-metric spaces. Besides, we construct an example and deduce several related results to demonstrate the usability of our derived theorem. As a consequence of this study, we deliver a fixed point result and also a result on the existence of solution of a type of integral equation. Additionally, we point out some mistakes in a recent paper by Aydi et al. [Nonlinear Anal. Model. Control 21 (2016), no. 1, 40-56].

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How to Cite this Article:

Poom Kumam, Surajit Karmakar, Lakshmi Kanta Dey, Ankush Chanda, Best proximity results for cyclic α-implicit contractions in quasi-metric spaces and its consequences, Advances in Fixed Point Theory, Vol 7, No 3 (2017), 342-358

Copyright © 2017 Poom Kumam, Surajit Karmakar, Lakshmi Kanta Dey, Ankush Chanda. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advances in Fixed Point Theory

ISSN: 1927-6303

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