Interpolative Reich–Rus–?iri? Type Contractions on Partial Metric Spaces

Erdal Karapinar, Ravi Agarwal and Hassen Aydi
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Erdal Karapinar: Department of Mathematics, Atilim University, Incek 06836, Ankara, Turkey
Ravi Agarwal: Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA
Hassen Aydi: College of Education in Jubail, Department of Mathematics, Imam Abdulrahman Bin Faisal University, P.O. 12020, Industrial Jubail 31961, Saudi Arabia

Mathematics, 2018, vol. 6, issue 11, 1-7

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–?iri? 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.

Keywords: partial metric; interpolative Reich–Rus–?iri? type contraction; fixed point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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