Fixed point results of a new family of hybrid contractions in generalised metric space with applications

Abstract

In this manuscript, a novel general family of contraction, called hybrid-interpolative Reich-Istr$ \breve{a}ţ $escu-type $ (G $-$ \alpha $-$ \mu) $-contraction is introduced and some fixed point results in generalised metric space that are not deducible from their akin in metric spaces are obtained. The preeminence of this class of contraction is that its contractive inequality can be extended in a variety of manners, depending on the given parameters. Consequently, a number of corollaries that reduce our result to other well-known results in the literature are highlighted and analysed. Substantial examples are constructed to validate the assumptions of our obtained theorems and to show their distinction from corresponding results. Additionally, one of our obtained corollaries is applied to set up unprecedented existence conditions for solution of a family of integral equations.

Keywords

• g-metric
• fixed point
• hybrid contraction
• integral equation