# On the prolongation of convex functions of higher order

## Abstract

This is the paper where the B-splines on nonuniform grid are introduced and studied for the first time. The recurrence formula and knot insertion formula are also dealt with.

## Original title (in French)

Sur le prolongement des fonctions convexes d’ordre superieur

## Keywords

B-splines; recurrence formula; knot insertion formula.

## Cite this paper as

T. Popoviciu, Sur le prolongement des fonctions convexes d’ordre superieur, Bull. Math. Soc. Roum. Sci., 36 (1934) no. 1, pp. 75-108.

## PDF

##### Journal

Bulletin mathématique de la Société Roumaine des Sciences

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## Notes on this paper

The results of T. Popoviciu were acknowledged by Carl de Boor and Alan Pinkus in their paper from 2003

• A. Pinkus and C. de Boor, The B-spline recurrence relations of Chakalov and of Popoviciu, J. Approx. Theory, 124 (2003) no. 1, pp. 115-123, doi: 10.1016/S0021-9045(03)00117-5