Best Proximity Points for Generalized α-ψ-Proximal Contractive Type Mappings

LetA andB be two nonempty subsets of ametric space (X, d). An element x ∈ A is said to be a fixed point of a given map T : A → B ifTx = x. Clearly,T(A)∩A ̸ = 0 is a necessary (but not sufficient) condition for the existence of a fixed point of T. If T(A) ∩ A = 0, then d(x, Tx) > 0 for all x ∈ A that is, the set of fixed points of T is empty. In a such situation, one often attempts to find an element x which is in some sense closest to Tx. Best proximity point analysis has been developed in this direction. An element a ∈ A is called a best proximity point of T if