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Open AccessArticle

On p-Cyclic Orbital M-K Contractions in a Partial Metric Space

1
Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai 600 062, Tamil Nadu, India
2
Department of Science and Humanities, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602 105, India
3
Faculty of Mathematics and Informatics, University of Plovdiv, “Paisii Hilendarski”, 24 Tzar Assen str., Plovdiv 4000, Bulgaria
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(7), 116; https://doi.org/10.3390/math6070116
Received: 15 June 2018 / Revised: 29 June 2018 / Accepted: 6 July 2018 / Published: 9 July 2018
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PDF [263 KB, uploaded 9 July 2018]

Abstract

A cyclic map with a contractive type of condition called p-cyclic orbital M-Kcontraction is introduced in a partial metric space. Sufficient conditions for the existence and uniqueness of fixed points and the best proximity points for these maps in complete partial metric spaces are obtained. Furthermore, a necessary and sufficient condition for the completeness of partial metric spaces is given. The results are illustrated with an example. View Full-Text
Keywords: contraction; p-cyclic mappings; best proximity point; partial metric space contraction; p-cyclic mappings; best proximity point; partial metric space
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 (CC BY 4.0).
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Gunasekar, T.; Karpagam, S.; Zlatanov, B. On p-Cyclic Orbital M-K Contractions in a Partial Metric Space. Mathematics 2018, 6, 116.

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