Probabilistic (ω,γ,ϕ)-contractions and coupled coincidence point results

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.

Keywords

• had${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over z} }}$ić type $ t $-norm
• probabilistic (ω
• γ
• ϕ)-contraction
• coupled coincidence point
• ordered menger pm-space