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

Abstract

Let (X,d) be a metric space and A₁, A₂, ..., A_p be nonempty subsets of X. We introduce a self map T on X, called p-cyclic orbital contraction map on the union of A₁, A₂, ..., A_p and obtain a unique best proximity point of T. That is, a point x ∈ ∪_i=1^pA_i such that d(x,Tx) = dist(A_i, A_i+1), 1 ≤ i ≤ p, where dist(A_i, A_i+1) = inf d(x,y: x ∈ A_i, y ∈ A_i+1).