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Mathematics 2018, 6(11), 256; https://doi.org/10.3390/math6110256

Interpolative Reich–Rus–Ćirić Type Contractions on Partial Metric Spaces

1
Department of Mathematics, Atilim University, Incek 06836, Ankara, Turkey
2
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
3
Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA
4
College of Education in Jubail, Department of Mathematics, Imam Abdulrahman Bin Faisal University, P.O. 12020, Industrial Jubail 31961, Saudi Arabia
*
Author to whom correspondence should be addressed.
Received: 23 October 2018 / Revised: 13 November 2018 / Accepted: 14 November 2018 / Published: 16 November 2018
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
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Abstract

By giving a counter-example, we point out a gap in the paper by Karapinar (Adv. Theory Nonlinear Anal. Its Appl. 2018, 2, 85–87) where the given fixed point may be not unique and we present the corrected version. We also state the celebrated fixed point theorem of Reich–Rus–Ćirić in the framework of complete partial metric spaces, by taking the interpolation theory into account. Some examples are provided where the main result in papers by Reich (Can. Math. Bull. 1971, 14, 121–124; Boll. Unione Mat. Ital. 1972, 4, 26–42 and Boll. Unione Mat. Ital. 1971, 4, 1–11.) is not applicable. View Full-Text
Keywords: partial metric; interpolative Reich–Rus–Ćirić type contraction; fixed point partial metric; interpolative Reich–Rus–Ćirić type contraction; fixed point
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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Karapinar, E.; Agarwal, R.; Aydi, H. Interpolative Reich–Rus–Ćirić Type Contractions on Partial Metric Spaces. Mathematics 2018, 6, 256.

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