Quasiconvex functions of higher order and the behavior of some nonlinear functionals


A result of T. Popoviciu, which characterizes real linear functionals on \(C(I)\) that are positive on n-convex functions as divided differences, is extended to the case of quasiconvex functions of order n to characterize on C(I)∩F-1(-∞,0) those real linear functionals F which are homogeneous for positive multipliers and sublinear.


Radu Precup
Babeş-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania




Cite this paper as:

R. Precup, Quasiconvex functions of higher order and the behavior of some nonlinear functionals, Anal. Numér. Théor. Approx., 21 (1992) no. 2, pp. 191-193.

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Mathematica – Revue d’Analyse Numerique et de la Theorie de l’Approximation
L’Analyse Numérique et la Théorie de l’Approximation
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Academia Republicii S.R.


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[1] Popoviciu, E., Sur une allure de quasi-convexité d’ordre supérieure, Mathematica, Rev. Anal. Numér. The’or. Approx., Anal. Numeŕ. théor. Approx., 11, pp. 129-137 (1982).

[2] Popoviciu, E., Teoreme de medie din analiza matematică şi legătura lor cu teoria interpolării. Ed. Dacia, Cluj, 1972.

[3] Popoviciu, T., Notes sur les fonctions convexes d’ordre supérieur (IX), Bull. Math. de la Soc. Roumaine des Sci., 43, pp. 85-141 (1941).

[4] Precup, R., On the quasiconvex functions of higher order, “Babeş-Bolyai” Univ., Preprint Nr. 6, pp. 275-282 (1989).


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