Best proximity results for cyclic α-implicit contractions in quasi-metric spaces and its consequences
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].
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.
Cite this article
P. Kumam, S. Karmakar, L. K. Dey, A. Chanda, Best proximity results for cyclic α-implicit contractions in quasi-metric spaces and its consequences, Adv. Fixed Point Theory 7 (2017), 342–358.
BibTeX
@article{Kumam2017,
author = {Kumam, Poom and Karmakar, Surajit and Dey, Lakshmi Kanta and Chanda, Ankush},
title = {Best proximity results for cyclic α-implicit contractions in quasi-metric spaces and its consequences},
journal = {Adv. Fixed Point Theory},
volume = {7},
year = {2017},
pages = {342--358},
doi = {}
}