Let us consider a pair (A, B) of nonempty subsets of a metric space X and a mapping T : A → B. In this article, we introduced a notion called P−property and used it to prove sufficient conditions for the existence of a point x0 ∈ A, called best proximity point, satisfying d(x0, Tx0) = dist(A, B) := inf{d(a, b) : a ∈ A, b ∈ B}.
