On the weak form of Ekeland's Variational Principle in quasi-metric spaces

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2015

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Elsevier

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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

We show that a quasi-metric space is right K-sequentially complete if and only if it satisfies the property of the weak form of Eke land's Variational Principle. This result solves a question raised by S. Cobzas (2011) [3]. (C) 2015 Elsevier B.V. All rights reserved.

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KARAPINAR, ERDAL/0000-0002-6798-3254; Romaguera, Salvador/0000-0001-7857-6139

Keywords

Quasi-metric space, Right K-sequentially complete, Ekeland's Variational Principle, Caristi's fixed point theorem

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25

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Volume

184

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Start Page

54

End Page

60

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https://doi.org/10.1016/j.topol.2015.01.011
 https://hdl.handle.net/20.500.14411/702

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