Necessary and sufficient conditions for generalized convexity
Annales Polonici Mathematici (1995)
- Volume: 61, Issue: 1, page 77-88
- ISSN: 0066-2216
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Abstract
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topJanusz Krzyszkowski. "Necessary and sufficient conditions for generalized convexity." Annales Polonici Mathematici 61.1 (1995): 77-88. <http://eudml.org/doc/262249>.
@article{JanuszKrzyszkowski1995,
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.},
author = {Janusz Krzyszkowski},
journal = {Annales Polonici Mathematici},
keywords = {generalized convexity; unrestricted n-parameter family; real-valued functions},
language = {eng},
number = {1},
pages = {77-88},
title = {Necessary and sufficient conditions for generalized convexity},
url = {http://eudml.org/doc/262249},
volume = {61},
year = {1995},
}
TY - JOUR
AU - Janusz Krzyszkowski
TI - Necessary and sufficient conditions for generalized convexity
JO - Annales Polonici Mathematici
PY - 1995
VL - 61
IS - 1
SP - 77
EP - 88
AB - 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.
LA - eng
KW - generalized convexity; unrestricted n-parameter family; real-valued functions
UR - http://eudml.org/doc/262249
ER -
References
top- [1] E. F. Beckenbach, Generalized convex functions, Bull. Amer. Math. Soc. 43 (1937), 363-371. Zbl0016.35202
- [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. Zbl0085.04505
- [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. Zbl0040.02901
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