New fixed point theorems for \(\theta\)-\(\phi\)-contraction on \(b\)-metric spaces

Volume 29, Issue 1, pp 12--27 http://dx.doi.org/10.22436/jmcs.029.01.02

Publication Date: August 11, 2022 Submission Date: February 07, 2022 Revision Date: February 15, 2022 Accteptance Date: March 10, 2022

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Authors

M. Rossafi - LaSMA Laboratory Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University Sidi Mohamed Ben Abdellah, B. P. 1796 Fes Atlas, Morocco. A. Kari - AMS Laboratory, Faculty of Sciences, Ben M'Sik, Hassan II University, Casablanca, Morocco. C. Park - Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea. J. R. Lee - Department of Data Science, Daejin University, Kyunggi 11159, Korea.

Abstract

In this paper, we define \(\theta\)-\(\phi\)-contraction on a \(b\)-metric space into itself by extending \(\theta\)-\(\phi \)-contraction introduced by Zheng {et al.} [D. W. Zheng, Z. Y. Cai, P. Wang, J. Nonlinear Sci. Appl., \(\bf 10\) (2017), 2662--2670] in metric space and also, we prove \(\theta \)-type theorem in the setting of \(b\)-metric spaces as well as \(\theta\)-\(\phi \)-type theorem in the framework of \(b\)-rectangular metric spaces. Moreover, we give some applications to nonlinear integral equations. We also give illustrative examples to exhibit the utility of our results.

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Keywords

• Fixed point
• rectangular \(b\)-metric space
• \(\theta\)-\(\phi\)-contraction

MSC

•  47H10
•  54H25

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