In this paper, we obtain some common fixed point theorems for recently introduced notion of PD-operators on a set X equipped with the function F 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], Bhatt et al.[Common Fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Non-linear analysis Theory, Methods and appl. 73(2010) 176-182] and several others.