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ArticleOriginal scientific text

Title

Necessary and sufficient conditions for generalized convexity

Authors 1

Affiliations

  1. Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland

Abstract

We give some necessary and sufficient conditions for an n-1 times differentiable function to be a generalized convex function with respect to an unrestricted n-parameter family.

Keywords

ENG
generalized convexity, unrestricted n-parameter family

Bibliography

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  2. D. Brydak, Application of generalized convex functions to second order differential inequalities, in: General Inequalities 4 (4th International Conference on General Inequalities, Oberwolfach, 1983), W. Walter (ed.), Birkhäuser, 1984, 297-305.
  3. P. Hartman, Unrestricted n-parameter families, Rend. Circ. Mat. Palermo (2) 7 (1958), 123-142, MR 21#4211.
  4. J. Krzyszkowski, On the generalized convex functions with respect to the three-parameters family of functions, Rocznik Naukowo-Dydaktyczny WSP w Krakowie, Prace Matematyczne XII, 115 (1987), 47-61.
  5. L. Tornheim, On n-parameter families of functions and associated convex functions, Trans. Amer. Math. Soc. 69 (1950), 457-467.
Annales Polonici Mathematici
1995/61/1
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Pages:
77-88
Main language of publication
English
Received
1993-12-02
Accepted
1994-05-15
Published
1995
Exact and natural sciences