engleski

On superquadratic functions

Recently a new interesting class of functions strongly related to convex functions has been introduced. It is named superquadratic functions. We say that the function ϕ is superquadratic if for any x≥ 0 there exists C(x)∈ R such that ϕ (y)≥ ϕ (x)+C(x)(y-x)+ϕ (|y-x|), ∀ y≥ 0. It can be proved that a superquadratic function which is also nonnegative is convex. Using some established characterisations and properties of this new class of functions we obtain variants of several well known inequalities for superquadratic functions. In a special case when superquadratic function is nonnegative we get refinements of known results related to convex functions.

convex functions; Hermite-Hadamard's inequality; Jensen's inequality; superquadratic functions

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