Naslov
Interpolation polinomials and inequalities for convex functions of higher order

Autori
Pečarić Josip ; Čuljak, Vera

Izvornik
Mathematical Inequalities & Applications (1331-4343) 5 (2002), 3; 369-386

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

Ključne riječi
Jensen inequality; Hadamard inequality; Petrovi\3; inequality; Giaccardi's inequality; Lidstone polinomial; Hermite interpolating polinomial; Abel-Gontscharoff interpolating polynomial; (n)-convex function

Sažetak
In this paper we prove several inequalities for convex function of a higher order. Generalizations of Hadamard's inequalities and the conversion of Jensen's inequality for (n)-convex function and with conditions on the regular, real (signed) Borel measure are presented by Lidstone's and Hermite's interpolating polinomials. As a discrete form we also obtain a generalization of Perović's inequality, i.e. Giaccardi's inequality. 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, to some inequalities related with Hadamard's and Petrović's inequalities.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA