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SUPERQUADRATIC FUNCTIONS AND REFINEMENTS OF SOME CLASSICAL INEQUALITIES
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 Title & Authors
SUPERQUADRATIC FUNCTIONS AND REFINEMENTS OF SOME CLASSICAL INEQUALITIES
Banic, Senka; Pecaric, Josip; Varosanec, Sanja;
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 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;
 Language
English
 Cited by
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 References
1.
S. Abramovich, S. Banic, and M. Matic, Superquadratic functions in several variables, J. Math. Anal. Appl. 327 (2007), no. 2, 1444-1460 crossref(new window)

2.
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

3.
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

4.
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

5.
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

6.
G. Sinnamon, Refining the Holder and Minkowski inequalities, J. Inequal. Appl. 6 (2001), no. 6, 633-640 crossref(new window)