# COMMON COUPLED FIXED POINT RESULTS FOR HYBRID PAIR OF MAPPING UNDER GENERALIZED (��, ��, ��)-CONTRACTION WITH APPLICATION

Handa, Amrish

• Accepted : 2019.07.18
• Published : 2019.08.31
• 13 6

#### Abstract

We introduce (CLRg) property for hybrid pair $F:X{\times}X{\rightarrow}2^X$ and $g:X{\rightarrow}X$. We also introduce joint common limit range (JCLR) property for two hybrid pairs $F,G:X{\times}X{\rightarrow}2^X$ and $f,g:X{\rightarrow}X$. We also establish some common coupled fixed point theorems for hybrid pair of mappings under generalized (${\psi},{\theta},{\varphi}$)-contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. As an application, we study the existence and uniqueness of the solution to an integral equation. We also give an example to demonstrate the degree of validity of our hypothesis. The results we obtain generalize, extend and improve several recent results in the existing literature.

#### Keywords

coupled fixed point;coupled coincidence point;generalized (${\psi},{\theta},{\varphi}$)-contraction;w-compatibility;F-weakly commuting;integral equation