Superquadratic functions and refinements of some classical inequalities
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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.
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.
참고문헌 (6)
- S. Abramovich, "Superquadratic functions in several variables", Journal of Mathematical Analysis and Applications, 327(2), pp.1444~1460 (2007)
- S. Abramovich, "Refining Jensen’s Inequality", Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie (N.S.), 47(1), pp.3~14 (2004)
- S. Abramovich, "Inequalities for averages of convex and superquadratic functions", Journal of Inequalities in Pure and Applied Mathematics, 5(4) (2004)
- D. S. Mitrinovic, "Classical and New Inequalities in Analysis, Mathematics and its Applications (East European Series)", pp.61~ (1993), Kluwer Academic Publishers Group
- J. E. Pecaric, "Convex Functions, Partial Orderings, and Statistical Applications, Mathematics in Science and Engineering", pp.187~ (1992), Academic Press, Inc.
- G. Sinnamon, "Refining the Holder and Minkowski inequalities", Journal of Inequalities and Applications, 6(6), pp.633~640 (2001)