Abstract
In this work, we show the existence of a coupled coincidence point and a coupled common fixed point for a ϕ-contractive mapping in G-metric spaces without the mixed g-monotone property, using the concept of a ( F ∗ ,g)-invariant set. We also show the uniqueness of a coupled coincidence point and give some examples, which are not applied to the existence of a coupled coincidence point by using the mixed g-monotone property. Further, we apply our results to the existence and uniqueness of a coupled coincidence point of the given mapping in partially ordered G-metric spaces.
Highlights
In, the existence and uniqueness of a fixed point for contraction type of mappings in partially ordered complete metric spaces has been first considered by Ran and Reurings [ ]
Afterwards, Bhaskar and Lakshmikantham [ ] introduced the concept of the mixed monotone property and proved some coupled fixed point theorems for mappings satisfying the mixed monotone property in partially ordered metric spaces
As a continuation of this work, several results of a coupled fixed point and a coupled coincidence point have been discussed in the recent literature
Summary
In , the existence and uniqueness of a fixed point for contraction type of mappings in partially ordered complete metric spaces has been first considered by Ran and Reurings [ ]. Afterwards, Bhaskar and Lakshmikantham [ ] introduced the concept of the mixed monotone property and proved some coupled fixed point theorems for mappings satisfying the mixed monotone property in partially ordered metric spaces.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
