Common fixed-point theorems for hybrid generalized $(F, ϕ)$ -contractions under the common limit range property with applications ......................

Abstract

We consider a relatively new hybrid generalized $F$ -contraction involving a pair of mappings and use this contraction to prove a common fixed-point theorem for a hybrid pair of occasionally coincidentally idempotent mappings satisfying generalized $(F, \varphi)$-contraction condition with the common limit range property in complete metric spaces. A similar result involving a hybrid pair of mappings satisfying the rational-type Hardy – Rogers $(F, \varphi)$-contractive condition is also proved. We generalize and improve several results available from the existing literature. As applications of our results, we prove two theorems for the existence of solutions of certain system of functional equations encountered in dynamic programming and the Volterra integral inclusion. Moreover, we provide an illustrative example.