W-distance based ϕ-coupled fixed point problem: Solution, well-posedness and applications to integral and functional equations

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Abstract In this paper we solve a fixed point problem formulated through a combination of three different contemporary trends in fixed point theory, namely, φ-fixed point results, coupled fixed point results and the use of w-distances. We have cited examples to illustrate our main theorem and to demonstrate how our theorem generalizes some known theorems and augments the domain of applicability of our result to a larger family of functions compared to these previous results. Well-posedness property of the problem is established. In a separate section we discuss two different applications of our result to problems of integral equations and functional equations.