A Note on Caristi-Type Cyclic Maps: Related Results and Applications

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2013

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Du, Wei-Shih
Karapınar, Erdal
Karapinar, Erdal

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Springer international Publishing Ag

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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

In this note, we first introduce the concept of Caristi-type cyclic map and present a new convergence theorem and a best proximity point theorem for Caristi-type cyclic maps. It should be mentioned that in our results, the dominated functions need not possess the lower semicontinuity property. Some best proximity point results and convergence theorems in the literature have been derived from our main results. Consequently, the presented results improve, extend and generalize some of the existence results on the topic.

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KARAPINAR, ERDAL/0000-0002-6798-3254
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best proximity point, Caristi-type cyclic map, MT-function (R-function), MT-cyclic contraction, Caristi-type fixed point theorem

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13

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https://doi.org/10.1186/1687-1812-2013-344
 https://hdl.handle.net/20.500.14411/106

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