Coincidence and fixed points of nonlinear Hybrid contractions

Abstract

In this Der, we show the existence of solutions of functional equations fx ∈ sx∩tx and x=fx ∈ sx∩Tx under certain contraction and asymptotic regularity conditions, where f, S and T are single‐valued and multl‐valued mappings on a metric space, respectively. We also observe that MukherJee′s fixed point theorem for a single‐valued mapping commuting with a multl‐valued mapping admits of a counterexample and suggest some modifications. While doing so, we also answer an open question raised in [I] and [2]. Moreover, our results extend and unify a multitude of fixed point theorems for multi‐valued mappings.