Necessary and sufficient conditions for generalized convexity

• Autorzy: Janusz Krzyszkowski
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

generalized convexity; unrestricted n-parameter family

Kategorie tematyczne

• 26A51: Convexity, generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1995
• Tom: 61
• Numer: 1
• Strony: 77-88

Daty

wydano

1995

otrzymano

1993-12-02

poprawiono

1994-05-15

poprawiono

1994-12-08

Twórcy

autor

Janusz Krzyszkowski

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

Bibliografia

• [1] E. F. Beckenbach, Generalized convex functions, Bull. Amer. Math. Soc. 43 (1937), 363-371.
• [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.