VARIANTS OF F-CONTRACTIONS AND EXISTENCE RESULTS OF INTEGRAL EQUATIONS

Abstract

In this paper, the concept of admissible hybrid F-(G-α-ϕ)-contraction is initiatedand new conditions for the existence of fixed points for such family of contractions areexamined in the setting of generalized metric spaces. It is noted that the principal ideasinvestigated herein improves and harmonizes some existing fixed point results in the relatedliterature. A few consequences of the presented main notion are highlighted and analyzedwith respect to the available brochure. To substantiate the assumptions and demonstratethe importance of the obtained results, a nontrivial and comparative example is constructed.It is observed that the ideas established in this work cannot be inferred from their analoguesin either metric or quasi-metric spaces. From application standpoint, one of the deducedcorollaries is applied to discuss and ascertain new conditions for the existence and uniquenessof solutions to certain class of nonlinear integral equations.