Naslov
On some inequalities for convex functions of higher order II

Autori
Pečarić, Josip ; Čuljak, Vera ; Rogina, Mladen

Izvornik
Nonlinear Analisys: Theory, Methods and Applications (0362-546X) 45 (2001); 281-294

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Jensen inequality; Hadamard inequality; Petrović inequality; Hermite's polynomial; (n)-convex function

Sažetak
In this paper we prove some inequalities for convex function of higher order. The well known Hermite interpolating polynomial leads us to a converse of Jensen inequality for a regular, signed measure and, as a consequence, a generalization of Hadamard and Petrović's inequalities. Also, we obtain a new upper bound for the error function of the Hermite interpolating polynomial|eH(x)| in terms of different norm ni of ||f^(n)||ni, resulting in a generalization of Mahajani inequality for different norm ni.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA