A COMMON FIXED POINT THEOREM OF INTEGRAL TYPE USING IMPLICIT RELATION

Abstract

In this paper, we prove a common fixed point theorem for two pairs of weakly compatible mappings in a metric space satisfying a contractive condition of integral type by using an implicit relation of Popa [7] and the property (E.A) introduced recently by Aamri and Mautawakil [1] as a generalization of noncompatible mappings. Our theorem generalizes Theorem 2 of Aamri and Mautawakil in the sense that we can obtain its contractive condition as an special case of our contractive condition. Further, our theorem is a slight variation of Theorem 5 of Popa in the sense that we have replaced the Meir-Keeler type contractive condition to impose the property (E.A). Thus we have unified and generalized both results by using implicit relation and property (E.A) under the integral type mappings.