The exact value of the error of a cubature formula is determined for some classes of continuous functions of two variables defined by strictly monotone moduli of continuity.
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S. M. Nikol’skii, Quadrature Formulas [in Russian], Nauka, Moscow (1979).
N. P. Korneichuk, Extremal Problems in Approximation Theory [in Russian], Nauka, Moscow (1976).
M. Sh. Shabozov, “Estimates for the error of quadrature formulas for some classes of functions,” Ukr. Mat. Zh., 43, No. 12, 1598–1601 (1991).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 4, pp. 572 – 576, April, 2009.
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Polyakov, O.V., Polyakova, N.O. Best cubature formulas for some classes of continuous functions of two variables. Ukr Math J 61, 687–693 (2009). https://doi.org/10.1007/s11253-009-0226-9
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DOI: https://doi.org/10.1007/s11253-009-0226-9