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On the Kolmogorov Problem for the Upper Bounds of Four Consecutive Derivatives of a Multiply Monotone Function

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Constructive Approximation Aims and scope

Abstract

In this paper we shall give necessary and sufficient conditions for the system of positive numbers \(M_{k_0}, M_{k_1}, M_{k_2}, M_{k_3}, 0=k_0<k_1<k_2<k_3=r,\) to guarantee the existence of the r-monotone function defined on the negative half-line such that \(\|x^{(k_i)}\|_{\infty}=M_{k_i}, i=0,1,2,3.\)

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Authors and Affiliations

  1. Department of Mathematical Analysis, Faculty of Mechanics and Mathematics, Dnepropetrovsk National University, ul. Naukova, 13, Dnepropetrovsk, 49050, Ukraine

    Vladislav Babenko

  2. Department of Mathematics and Statistics, Sam Houston State University, Box 2206, Huntsville, TX 77341, USA

    Yuliya Babenko

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  1. Vladislav Babenko
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  2. Yuliya Babenko
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Correspondence to Vladislav Babenko or Yuliya Babenko.

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Babenko, V., Babenko, Y. On the Kolmogorov Problem for the Upper Bounds of Four Consecutive Derivatives of a Multiply Monotone Function. Constr Approx 26, 83–92 (2007). https://doi.org/10.1007/s00365-006-0653-4

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  • DOI: https://doi.org/10.1007/s00365-006-0653-4

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