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J. Korean Math. Soc. 2008; 45(2): 513-525
Printed March 1, 2008
Copyright © The Korean Mathematical Society.
Superquadratic functions and refinements of some classical inequalities
Senka Banic, Josip Pecaric, and Sanja Varosanec
University of Split, University of Zagreb, University of Zagreb
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 Petrovi\' c 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 functions, Giaccardi's inequality, Hermite-Hadamard's inequality, Jensen's inequality, superquadratic functions, sum of power $p$
MSC numbers: Primary 26D15
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