Coincidence point results and its applications in partially ordered metric spaces

The purpose of this paper is to establish some common fixed point theorems for $f$-nondecreasing self-mapping satisfying a certain rational type contraction condition in the frame of a metric spaces endowed with partial order. Also, some consequences of the results in terms of an integral type contractions are presented in the space. Further, the monotone iterative technique has been used to find a unique solution of an integral equation.