Probabilistic $ (\omega, \gamma, \phi) $-contractions and coupled coincidence point results

Manish Jain; Deepak Jain; Choonkil Park; Dong Yun Shin; Manish Jain; Deepak Jain; Choonkil Park; Dong Yun Shin

doi:10.3934/math.2021675

AIMS Mathematics

2021, Volume 6, Issue 11: 11620-11630. doi: 10.3934/math.2021675

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Research article

Probabilistic $ (\omega, \gamma, \phi) $-contractions and coupled coincidence point results

1.
Department of Mathematics, Ahir College, Rewari 123401, India
2.
Department of Mathematics, Deenbandhu Chottu Ram University of Science and Technology, Murthal, Sonepat, India
3.
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea
4.
Department of Mathematics, University of Seoul, Seoul 02504, Korea

Received: 07 April 2021 Accepted: 09 August 2021 Published: 11 August 2021
MSC : 47H10, 54H25

In this paper, we introduce the notion of probabilistic $ (\omega, \gamma, \phi) $-contraction and establish the existence coupled coincidence points for mixed monotone operators subjected to the introduced contraction in the framework of ordered Menger $ PM $-spaces with Had${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over z} }}$ić type $ t $-norm. As an application, a corresponding result in the setup of fuzzy metric space is also obtained.
Citation: Manish Jain, Deepak Jain, Choonkil Park, Dong Yun Shin. Probabilistic $ (\omega, \gamma, \phi) $-contractions and coupled coincidence point results[J]. AIMS Mathematics, 2021, 6(11): 11620-11630. doi: 10.3934/math.2021675

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Abstract

In this paper, we introduce the notion of probabilistic $ (\omega, \gamma, \phi) $-contraction and establish the existence coupled coincidence points for mixed monotone operators subjected to the introduced contraction in the framework of ordered Menger $ PM $-spaces with Had${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over z} }}$ić type $ t $-norm. As an application, a corresponding result in the setup of fuzzy metric space is also obtained.

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