engleski

Generalization of Jensen's inequality by Hermite polynomials and related results

In this note we consider n-convex functions. Using the hermite interpolating polynomials and conditions on the Green functions we present results for Jensen's inequality and converses of Jensen's inequality for signed measure. Motivated by obtained inequalities we define linear functionals and give mean value theorems for them. Finally, we apply obtained result to Stolarsky type means.

Jensen's inequality, Hermite polinomials, n-convex functions, Green function

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