# Convex functions of order $$n$$ and $$P_n$$-simple functionals

## Abstract

A certain characterization of convex functions of order $$n$$ on an interval $$I$$ which are $$(n+1)$$ times differentiable on $$I$$, by the use of a $$P_{n}$$-simple functional $$L$$, is proved to be in connection with a certain behaviour of the functional $$L$$ with respect to the strictly quasiconvex functions of order $$n-1$$. In context it is also proved that the necessary and sufficient condition for an $$n$$ times continuously differentiable real function $$f$$ be strictly quasiconvex of order $$n\ (n\geq 0)$$ on $$I$$ is that f be convex or concav e or order $$n$$ on $$I$$, or there exist $$c\in I$$ such that $$f$$ be concave of order $$n$$ on $$I\cap (-\infty,c)$$ and convex of order $$n$$ on $$I\cap [c,+\infty]$$.

## Authors

University of Cluj-Napoca, Department of Mathematics, Cluj-Napoca, Romania

## PDF

##### Cite this paper as:

R. Precup, Convex functions of order $$n$$ and $$P_n$$-simple functionals, Rev. Anal. Numér. Théor. Approx., 18 (1989) no. 2, pp. 161-170.

##### Journal

Mathematica-Revue d’analyse numérique et de théorie de l’approximation

##### Print ISSN

Not available yet.

##### Online ISSN

Not available yet.

MR: 92d:41048.

## References

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