Common fixed point theorems for PDPD-operator pairs under relaxed conditions with applications

In this paper, we define PDPD-operator pair of single valued mappings and obtain some common fixed point theorems for this class of maps under relaxed conditions. Our theorem generalizes results of Bhatt et al. [A. Bhatt, H. Chandra, D.R. Sahu, Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Nonlinear Anal. 73 (2010) 176–182.], Jungck and Rhoades [G. Jungck, B.E. Rhoades, Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory 7 (2) (2006) 287–296.] and Hussain et al. [N. Hussain, M.A. Khamsi, A. Latif, Common fixed points for JHJH-operators and occasionally weakly biased pairs under relaxed conditions, Nonlinear Anal. 74 (2011) 2133–2140.] and others. As applications, we also study the solution of functional equations arising from dynamic programming and variational inequalities arises in two point obstacle problem. We also discuss some illustrative examples to highlight the realized improvements.