coincident and common fixed point theorems using comparison and admissible function in w-distance metric space

In this manuscript, the concept of generalized (η, χ, p) contractive mapping for two maps in the framework of w-distance is introduced and some fixed point results are established, which extend recent results of lakzian and rhoades [5] and many existing results in the literature. in addition, to validate the novelty of our findings, we give an illustrative example, which yields the main result. moreover, as an application, we employ the achieved result to earn the existence criteria of the solution of a type of non-linear fredholm integral equation.