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.
@article{bwmeta1.element.bwnjournal-article-apmv61z1p77bwm,
author = {Janusz Krzyszkowski},
title = {Necessary and sufficient conditions for generalized convexity},
journal = {Annales Polonici Mathematici},
volume = {62},
year = {1995},
pages = {77-88},
zbl = {0829.26006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv61z1p77bwm}
}
Janusz Krzyszkowski. Necessary and sufficient conditions for generalized convexity. Annales Polonici Mathematici, Tome 62 (1995) pp. 77-88. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv61z1p77bwm/
[000] [1] E. F. Beckenbach, Generalized convex functions, Bull. Amer. Math. Soc. 43 (1937), 363-371. | Zbl 0016.35202
[001] [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.
[002] [3] P. Hartman, Unrestricted n-parameter families, Rend. Circ. Mat. Palermo (2) 7 (1958), 123-142, MR 21#4211. | Zbl 0085.04505
[003] [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.
[004] [5] L. Tornheim, On n-parameter families of functions and associated convex functions, Trans. Amer. Math. Soc. 69 (1950), 457-467. | Zbl 0040.02901