Interpolative Reich-Rus Type Contractions on Partial Metric Spaces

Karapinar, Erdal; Agarwal, Ravi; Aydi, Hassen

Interpolative Reich-Rus Type Contractions on Partial Metric Spaces

Date

2018

Authors

Karapinar, Erdal

Agarwal, Ravi

Aydi, Hassen

Publisher

Mdpi

Organizational Units

Organizational Unit

Mathematics

(2000)

The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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-Ciric 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.