Abel-Gontscharoff interpolating polynomial and some inequalities for convex functions of higher order

Josip Pecaric
Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000 Zagreb, Croatia
Vera Culjak
Department of mathematics
Faculty of Civil Engineering, University of Zagreb,
Kaciceva 26, 10000 Zagreb, Croatia

Abstract:

In this paper we prove some inequalities for convex function of a higher order. The Abel - Gontscharoff interpolating polynomial with two-point right focal conditions leads us to an inequality like converse of Jensen inequality for a regular, signed measure and, as a consequence, some generalization of Hadamard and Petrovic's inequalities.

Keywords: Jensen inequality, Hadamard inequality, Petrovic inequality, Abel - Gontscharoff interpolating polynomial,$(n)$-convex function.