Abstract
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.
Authors
Radu Precup
Babeş-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania
Keywords
Cite this paper as:
R. Precup, Quasiconvex functions of higher order and the behavior of some nonlinear functionals, Rev. Anal. Numér. Théor. Approx., 21 (1992) no. 2, pp. 191-193.
About this paper
Journal
Revue d’analyse numérique et de théorie d’approximation
Publisher Name
Academia Republicii S.R.
DOI
Not available yet.
Print ISSN
Not available yet.
Online ISSN
Not available yet.
Google Scholar Profile
References
[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).