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

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

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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.

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Journal

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

Publisher Name

Academia Republicii S.R.

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MR: 92d:41048.

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References

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