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SUPERQUADRATIC FUNCTIONS AND REFINEMENTS OF SOME CLASSICAL INEQUALITIES
Banic, Senka,Pecaric, Josip,Varosanec, Sanja Korean Mathematical Society 2008 대한수학회지 Vol.45 No.2
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.
Superquadratic functions and refinements of some classical inequalities
Senka Banic,Josip Pecaric,Sanja Varosanec 대한수학회 2008 대한수학회지 Vol.45 No.2
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. 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.
Positivity of sums for n−convex functions via Taylor’s formula and Green function
A. R. KHAN,J. PECARIC,M. PRALJAK,S. VAROSANEC 장전수학회 2017 Advanced Studies in Contemporary Mathematics Vol.27 No.4
Conditions under which the inequality ∑mi=1 pif(xi) ≥ 0 holds for every n-convex function f are considered. We are using two approaches: one by the Taylor formula and other using the Green function. Integral analogues and some related results for n-convex functions at a point are also given, as well as bounds for the integral remainders which occur in identities associated with the obtained inequalities.