Fixed Point Results of Jaggi-Type Hybrid Contraction in Generalized Metric Space

Abstract

In this manuscript, a new family of contractions called Jaggi-type hybrid <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mfenced open="(" close=")"> <a:mrow> <a:mi>G</a:mi> <a:mo>−</a:mo> <a:mi>ϕ</a:mi> </a:mrow> </a:mfenced> </a:math> -contraction is introduced and some fixed point results in generalized metric space that are not deducible from their akin in metric space are obtained. The preeminence of this class of contractions is that its contractive inequality can be extended in a variety of manners, depending on the given parameters. Consequently, several corollaries that reduce our result to other well-known results in the literature are highlighted and analyzed. 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 the solution of a family of integral equations.