Browse > Article
http://dx.doi.org/10.4134/JKMS.2008.45.2.513

SUPERQUADRATIC FUNCTIONS AND REFINEMENTS OF SOME CLASSICAL INEQUALITIES  

Banic, Senka (FACULTY OF CIVIL ENGINEERING AND ARCHITECTURE UNIVERSITY OF SPLIT)
Pecaric, Josip (FACULTY OF TEXTILE TECHNOLOGY UNIVERSITY OF ZAGREB)
Varosanec, Sanja (DEPARTMENT OF MATHEMATICS UNIVERSITY OF ZAGREB)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.2, 2008 , pp. 513-525 More about this Journal
Abstract
Using known properties of superquadratic functions we obtain a sequence of inequalities for superquadratic functions such as the Converse and the Reverse Jensen type inequalities, the Giaccardi and the Petrovic type inequalities and Hermite-Hadamard's inequalities. Especially, when the superquadratic function is convex at the same time, then we get refinements of classical known results for convex functions. Some other properties of superquadratic functions are also given.
Keywords
convex function; Giaccardi's inequality; Hermite-Hadamard's inequality; Jensen's inequality; superquadratic functions; sum of power p;
Citations & Related Records

Times Cited By Web Of Science : 5  (Related Records In Web of Science)
Times Cited By SCOPUS : 5
연도 인용수 순위
1 J. E. Pecaric, F. Proschan, and Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Mathematics in Science and Engineering, 187. Academic Press, Inc., Boston, MA, 1992
2 S. Abramovich, S. Banic, and M. Matic, Superquadratic functions in several variables, J. Math. Anal. Appl. 327 (2007), no. 2, 1444-1460   DOI   ScienceOn
3 S. Abramovich, G. Jameson, and G. Sinnamon, Refining Jensen's Inequality, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 47 (95) (2004), no. 1-2, 3-14
4 S. Abramovich, G. Jameson, and G. Sinnamon, Inequalities for averages of convex and superquadratic functions, JIPAM. J. Inequal. Pure Appl. Math. 5 (2004), no. 4, Article 91
5 D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Classical and New Inequalities in Analysis, Mathematics and its Applications (East European Series), 61. Kluwer Academic Publishers Group, Dordrecht, 1993
6 G. Sinnamon, Refining the Holder and Minkowski inequalities, J. Inequal. Appl. 6 (2001), no. 6, 633-640   DOI