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Tytuł artykułu
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Abstrakty
This paper presents a differential criterion of n dimensional geometrically convex functions, and gives some applications.
Wydawca
Czasopismo
Rocznik
Tom
Strony
197--208
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
autor
- Zhejiang Haining. Tv University, Haining, Zhejiang 3144000, P. R. China, zjzxm79@sohu.com
Bibliografia
- [1] Bernstein, F., Doetsch, G., Zur Theorie der Konvexen Functionen, Math. Ann. 16 (1915), 514-526.
- [2] Daroczy, Z., Pales, Zs., Convexity with given infinite weight sequences, Stochastica 11 (1987), 5-12.
- [3] Jarczyk, W., Matkowski, J., On Mulholland's inequality, Proc. Amer. Math. Soc. 130(11) (2002), 3243-3247 (electronic).
- [4] Kuang, J. C., Applied Inequalities (in Chinese), 3rd ed., Shandong Science and Techology Press, Jinan, 2004.
- [5] Kuczma, M., An Introduction to the Theory of Functional Equations and Inequalities, Pr. Nauk. Uniw. Śl. Katow. 489, Silesian University, Katowice, PWN, Warsaw, 1985.
- [6] Marshall, A. W., Inequalities: Theory of Majorization and its Applications, Math. Sci. Engrg. 143, Academic Press, Inc., New York-London, 1979.
- [7] Matkowski, J., LP-like paranorms, "Selected topics in functional equations and iteration theory" (Graz, 1991), Grazer Math. Ber. 316 (1992), 103-138.
- [8] Matkowski, J., Private communications, (2006).
- [9] Mitrinovic, D. S., Pecaric, J. E., Fink, A. -M., Classical and New Inequalities in Analysis, Kluwer Academic Publishers Group, Dordrecht, 1993.
- [10] Montel, P., ,Sur les functions convexes et les fonctions sousharmoniques, J. Math. Pures Appl. (9) 7 (1928), 29-60.
- [11] Niculescu, C. P., Convexity according to the geometric mean, Math. Inequal. Appl. 3(2) (2000), 155-167.
- [12] Sierpinski, W., Sur les fonctions convexes mesurables, Fund. Math. 1 (1920), 125-128.
- [13] Stolarsky, K. B., Generalizations of the logarithmic mean, Math. Mag. 48 (1975), 87-92.
- [14] Yang, D.-H., About inequality of geometric convex function (in Chinese), J. Hebei Teachers College Nat. Sci. Ed. 22(4) (2002), 325-328.
- [15] Zhang, X.-M., Geometrically Convex Function (in Chinese), An'hui University Press. Hefei, 2004.
- [16] Zhang, X.-M., An inequality of the Hadamard type for the geometrica convex functions (in Chinese), Math. Practice Theory 34(9) (2004), 171-176.
- [17] Zhang, X.-M., Some theorem on geometric convex function and its applictions (in Chinese), J. Capital Norm. Univ. 25(2) (2004), 11-.13.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD6-0002-0037