Best proximity points of p-cyclic orbital Meir–Keeler contraction maps

The importance of Mathematics lies in solving equations of the form f(x) = 0. This equation can also be written as f(x) = g(x)−x for some suitable function g. Finding the solution of the equation f(x) = 0 is equivalent to finding the solution of the equation g(x) = x. Theorems, which provide a theory by enhancing the possibilities for the existence of a solution to the given equation g(x) = x, are called fixed point theorems. One such theorem is the famous Banach contraction theorem. It stats that “if (X, d) is a complete metric space and T is a self map on X such that there exists a k, 0 < k < 1, such that d(Tx, Ty) 6 kd(x, y) for all x, y ∈ X , then, for any ξ ∈ X , {Tξ} converges to a unique fixed point. One of the interesting extensions of the classical Banach contraction theorem is Meir– Keeler contraction introduced by Meir and Keeler in [18]. Later, the authors of [16] introduced a class of mappings called cyclic contractive mappings. If (X, d) is a metric space and A1, A2, . . . , Ap (p > 2) are the nonempty