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Hermite-Hadamard-Fejer-Type Inequalities and Weighted Three-Point Quadrature Formulae

The goal of this paper is to derive Hermite- Hadamard-Fejer-type inequalities for higher-order convex functions and a general three-point integral formula involving harmonic sequences of polynomials and w-harmonic sequences of functions. In special cases, Hermite-Hadamard-Fejer-type estimates are derived for various classical quadrature formulae such as the Gauss-Legendre three-point quadrature formula and the Gauss- Chebyshev three-point quadrature formula of the first and of the second kind.

Hermite-Hadamard-Fejer inequalitiesweighted three-point formulaehigher-order convex functionsw-harmonic sequences of functionsharmonic sequences of polynomials

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