Best proximity points of p-cyclic orbital Meir–Keeler contraction maps - Karpagam, Saravanan; Zlatanov, Boyan (Nonlinear Analysis: Modelling and Control, 2016)
Let (X,d) be a metric space and A1, A2, ..., Ap 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, ..., Ap and obtain a unique best proximity point of T. That is, a point x ∈ ∪i=1pAi such that d(x,Tx) = dist(Ai, Ai+1), 1 ≤ i ≤ p, where dist(Ai, Ai+1) = inf d(x,y: x ∈ Ai, y ∈ Ai+1).
Keywords: uniformly convex Banach space; best proximity points; p-cyclic maps; orbital contractions