Abstract. Weighted version of two-point integral quadrature formula is obtained using w−harmonic sequences of functions. Improved version of Guessab and Schmeisser's result is given with new integral inequalities under various regular conditions. As special cases, the generalizations of quadrature formulae of Gauss type are established.

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Abstract. The weighted generalization of the integral formula with 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.Mathematics subject classification (2010): 26D15, 65D30, 65D32.

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