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manuscripta mathematica

, Volume 29, Issue 1, pp 29–47 | Cite as

Folgenkonvexe funktionen

  • Siegfried Gabler
Article

Abstract

In this paper functions f:(a,b)→R are considered with the property that for all n>2 and all x1,x2,...,xn∈(a,b)
is convex in k. Functions with this property are called sequentially convex. It is proved that if f is convex, twice differentiable, and f″ is convex then f is sequentially convex. In case f is a continous function defined on the whole ofR these conditions are necessary too.

Keywords

Number Theory Algebraic Geometry Topological Group Continous Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literatur

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    BOAS, R. P., Jr. and D. V. WIDDER: Functions with positive differences. Duke math. J. 7, 496–503 (1940)Google Scholar
  2. [2]
    CARLSON, B. C., MEANY, R. K. and S. A. NELSON: Mixed arithmetic and geometric means. Pacific J. Math. 38 343–349 (1971)Google Scholar
  3. [3]
    POPOVICIU, T.: Les fonctions convexes. Paris: Hermann 1944Google Scholar
  4. [4]
    POPOVICIU, T.: sur certaines inégalités qui caractérisent les fonctions convexes. An. Sti. Univ. Al. I Cuza Iasi, n. Ser., Sect. Ia 11B, 155–164 (1965)Google Scholar
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    ROBERTS, A. W. and D. E. VARBERG: Convex Functions. New York and London: Academic Press 1973Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Siegfried Gabler
    • 1
  1. 1.Seminar für Statistik der Universität MannheimMannheim 1 A 5

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