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Open AccessArticle

On Generalized (α, ψ, MΩ)-Contractions with w-Distances and an Application to Nonlinear Fredholm Integral Equations

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Department of Mathematics, Payame Noor University, Tehran 19395-4697, Iran
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Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339 Bojnord, Iran
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Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
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Université de Sousse, Institut Supérieur d’Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia
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China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
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Institute of Research and Development of Processes IIDP, University of the Basque Country, Campus of Leioa, P.O. Box 48940 Leioa (Bizkaia), Spain
*
Authors to whom correspondence should be addressed.
Symmetry 2019, 11(8), 982; https://doi.org/10.3390/sym11080982
Received: 14 June 2019 / Revised: 9 July 2019 / Accepted: 15 July 2019 / Published: 2 August 2019
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Abstract

The study of asymmetric structures and their applications in mathematics is interesting. One of the types of asymmetric structures on a metric space has been initiated by Kada et al. (1996) and is known as a w-distance. That lack of symmetry attracts many researchers in fixed point theory. In this manuscript, we introduce a new type of contraction named generalized ( α , ψ , M Ω ) -contractive mappings via w-distances, and then we prove some new related fixed point results, generalizing and improving the recent results of Lakzian et al. (2016) and others. At the end, we give some examples. To illustrate the usability of the new theory, we apply our obtained results to resolve a nonlinear Fredholm-integral-type equation. View Full-Text
Keywords: fixed point; w-distance; (α, ψ, MΩ)-contractive mapping; fredholm integral equation fixed point; w-distance; (α, ψ, MΩ)-contractive mapping; fredholm integral equation
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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Lakzian, H.; Barootkoob, S.; Mlaiki, N.; Aydi, H.; De la Sen, M. On Generalized (α, ψ, MΩ)-Contractions with w-Distances and an Application to Nonlinear Fredholm Integral Equations. Symmetry 2019, 11, 982.

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