A STUDY OF GENERALIZED PD-OPERATORS ON PROBABILISTIC METRIC SPACE

Abstract

In this paper, we introduce the notion of generalized P D-operator pair with order n for single valued mappings and obtain some common fixed point theorems for generalized PD-operators on a set X equipped with the function F : X × X → ∆ without using the triangle inequality besides relaxing symmetric condition. Our results extend the results of Pathak and Rai [Common fixed points for PD-operator pairs under relaxed conditions with applications, Journal of Computational and Applied Mathematics, 239(1) (2013), 103– 113], Hussain et al.[Common fixed points for JH-operators and occasionally weakly biased pairs under relaxed conditions, Nonlinear Anal., 74 (2011), 2133-2140], Sintunavarat and Poom [Common fixed point theorems for generalized JH-operator classes and invariant approximations, Journal of ineqalities and Applications, 67 (2011)] and several others.