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Large Contractions on Quasi-Metric Spaces with an Application to Nonlinear Fractional Differential Equations

1
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
2
Department of Mathematics and Computer Sciences, Universitatea Transilvania Brasov, 500036 Brasov, Romania
3
Department of Mathematics & Statistics, International Islamic University, Islamabad H-10 44000, Pakista
4
Institut Supérieur d’Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(5), 444; https://doi.org/10.3390/math7050444
Received: 22 February 2019 / Revised: 13 May 2019 / Accepted: 14 May 2019 / Published: 18 May 2019
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
PDF [241 KB, uploaded 18 May 2019]

Abstract

In this manuscript, we introduce a new notion: a Berinde type ( α , ψ ) -contraction mapping. Thereafter, we investigate not only the existence, but also the uniqueness of a fixed point of such mappings in the setting of right-complete quasi-metric spaces. The result, presented here, not only generalizes a number of existing results, but also unifies several ones on the topic in the literature. An application of nonlinear fractional differential equations is given.
Keywords: nonlinear fractional differential equations; Berinde type contraction; quasi-metric space; admissible mappings; fixed point nonlinear fractional differential equations; Berinde type contraction; quasi-metric space; admissible mappings; fixed point
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Karapınar, E.; Fulga, A.; Rashid, M.; Shahid, L.; Aydi, H. Large Contractions on Quasi-Metric Spaces with an Application to Nonlinear Fractional Differential Equations. Mathematics 2019, 7, 444.

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