engleski

Weighted version of general integral formula of the Euler type

The weighted generalization of the integral formula in m nodes is introduced, and some sharp and the best possible inequalities for the functions whose higher order derivatives belong to L_p spaces are given. Specially, the general one- point integral formula is established. Special cases of the well known weights are considered and generalizations of the Gaussian quadrature formulae with one node are obtained.

harmonic polynomials; weighted integral formula; one-point formula; w-Appell sequences; w-harmonic sequences; weight; Lp inequalities; Gauss rule; Euler identity

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