Some applications of Caristi’s fixed point theorem in metric spaces

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2016

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Springer International Publishing

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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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In this work, partial answers to Reich, Mizoguchi and Takahashi’s and Amini-Harandi’s conjectures are presented via a light version of Caristi’s fixed point theorem. Moreover, we introduce the idea that many of known fixed point theorems can easily be derived from the Caristi theorem. Finally, the existence of bounded solutions of a functional equation is studied. © 2016 Khojasteh et al.

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Boyd and Wong’s contraction, Caristi’s fixed point theorem, Hausdorff metric, Mizoguchi-Takahashi, Reich’s problem

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12

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Fixed Point Theory and Applications

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2016

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1

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https://doi.org/10.1186/s13663-016-0501-z
 https://hdl.handle.net/20.500.14411/3802

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