engleski

Generalization of Jensen's inequality by Hermite polynomials and related results

In this note, we consider convex functions of higher order. Using the Hermite's interpolating polynomials and conditions on the Green's functions the results concerning for the converse of Jensen's inequality for signed measure are presented. Using these inequalities, we produce new exponentially convex functions. Finally, we give several examples of the families of functions for which the obtained results can be applied.

Green function ; Jensen's inequality ; n-convex function ; Hermite interpolating polynomial ; Cauchy type mean value theorems ; n-exponential convexity ; exponential convexity ; log-convexity ; means

nije evidentirano