This paper deals with a new extension of Jensen's discrete inequality to a partially convex function f , which is defined on a real interval I, convex on a subinterval (a, b) ⊂ I, decreasing for u ≤ c and increasing for u ≥ c ,w herec ∈ (a, b). Several relevant applications are given to show the effectiveness of the proposed partially convex function theorem. MSC: 26D07; 26D10; 41A44