The paper deals with convex combinations, convex functions, and Jensen’s functionals. The main idea of this work is to present the given convex combination by using two other convex combinations with minimal number of points. For example, as regards the presentation of the planar combination, we use two trinomial combinations. Generalizations to higher dimensions are also considered.
Zlatko Pavić. Shanhe Wu. Štefanija Klarić. "Convex Combination Inequalities of the Line and Plane." Abstr. Appl. Anal. 2014 1 - 7, 2014. https://doi.org/10.1155/2014/916243