EXISTENCE AND UNIQUENESS OF BEST PROXIMITY POINTS UNDER RATIONAL CONTRACTIVITY CONDITIONS

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Date

2016

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Walter de Gruyter Gmbh

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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.

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Abstract

The main aim of this paper is to present some theorems in order to guarantee existence and uniqueness of best proximity points under rational contractivity conditions using very general test functions. To illustrate the variety of possible test functions, we include some examples of pairs of functions which are included in innovative papers published in the last years. As a consequence, we prove that our results unify and extend some recent results in this field.

Description

KARAPINAR, ERDAL/0000-0002-6798-3254; Roldán López de Hierro, Antonio Francisco/0000-0002-6956-4328

Keywords

best proximity point, fixed point, rational contractive condition, P-property, weak P-property

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Citation

9

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Volume

66

Issue

6

Start Page

1427

End Page

1442

URI

https://doi.org/10.1515/ms-2016-0234
 https://hdl.handle.net/20.500.14411/659

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