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Optimal renewal of definite integrals of monotone functions from the class H ω

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Abstract

We obtain an exact estimate of the error of optimal renewal of an integral on a set of functions f(t) monotone on [a, b] with a convex majorant of the modulus of continuity, provided that |f(b)−f(a)|=L>0.

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Authors
  1. T. N. Busarova
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Additional information

Dnepropetrovsk Technical University of Railway Transport, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 8, pp. 1011–1015, August, 1997.

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Busarova, T.N. Optimal renewal of definite integrals of monotone functions from the class H ω . Ukr Math J 49, 1135–1139 (1997). https://doi.org/10.1007/BF02487542

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  • DOI: https://doi.org/10.1007/BF02487542

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