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