Affine and Functional Form of Jensen's Inequalitiy for $3$-convex   Functions at a Point
  In this paper, we give the refinement of an extension of Jensen's inequality to affine combinations. Furthermore, we present the functional form of Jensen's inequality for continuous 3-convex functions of one variable at a point. 
Imran Abbas Baloch, Silvestru Sever Dragomir
math.CA