Extensions of recent combinatorial refinements of discrete and integral Jensen inequalities

Abstract The main purpose of this work is to present essential extensions results in [7] and [8], apply them some special situations. Of particular interest the refinement integral Jensen inequality for vector valued integrable functions. applications related four topics, namely f -divergences information theory (an interesting weighted geometric mean–arithmetic mean obtained as a consequence), norm inequalities, quasi-arithmetic means, Hölder’s Minkowski’s inequalities.