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

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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ISRP Style

M. Rossafi, A. Kari, C. Park, J. R. Lee, New fixed point theorems for \(\theta\)-\(\phi\)-contraction on \(b\)-metric spaces, Journal of Mathematics and Computer Science, 29 (2023), no. 1, 12--27

AMA Style

Rossafi M., Kari A., Park C., Lee J. R., New fixed point theorems for \(\theta\)-\(\phi\)-contraction on \(b\)-metric spaces. J Math Comput SCI-JM. (2023); 29(1):12--27

Chicago/Turabian Style

Rossafi, M., Kari, A., Park, C., Lee, J. R.. "New fixed point theorems for \(\theta\)-\(\phi\)-contraction on \(b\)-metric spaces." Journal of Mathematics and Computer Science, 29, no. 1 (2023): 12--27


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