Generalization of an integral formula of Guessab and Schmeisser (CROSBI ID 162330)
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Kovač, Sanja ; Pečarić, Josip
engleski
Generalization of an integral formula of Guessab and Schmeisser
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.
Weight function; W-harmonic sequences of functions; quadrature formula; Gauss formula; Legendre-Gauss; Chebyshev-Gauss; Hermite-Gauss; inequality; sharp constants; best possible constants; two-point quadrature formula.
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