Studia Informatica
Volume XXXIX, Number 3 (1994)
pp. 43 - 54

Divided differences and Convex Functions of Higher Order on Networks

M.-E. Iacob

Abstract. For any real function f defined on a connected subset of an oriented network, we are interested to find a way to introduce divided differences on n points. We give a representation theorem for the generalized divided differences and some properties resulting from this theorem. Next we introduce the concept of convex real function of order n, defined on network. Some properties of these functions will be studied in the last part of this paper.

Rezumat. - Diferente divizate si functii convexe de ordin superior in retele. In acest articol vom introduce diferentele divizate pe n puncte, pentru orice functie reala, definita pe o submultime conexa a unei retele. Este expusa o teorema de reprezentarea a acestor diferente divizate generalizate. Ultima sectiune este dedicata functiilor convexe de ordin n, definite pe retele si studiului unor proprietati ale acestui tip de functii.

AMS Subject Classifications. 52-02

Studia Universitatis "Babes-Bolyai" Cluj - Napoca