Ukrainian Mathematical Journal

, Volume 70, Issue 7, pp 1001–1011 | Cite as

On the Dependence of the Norm of a Multiply Monotone Function on the Norms of Its Derivatives

  • A. R. Bondarenko
  • O. V. Kovalenko

We establish necessary and sufficient conditions for a system of positive numbers \( {M}_{k_1},{M}_{k_2},{M}_{k_3},{M}_{k_4},0={k}_1<{k}_2<{k}_3\le r-3,{k}_4=r \), guaranteeing the existence of an (r − 2)-monotone function x in the half line such that \( {\left\Vert {x}^{\left({k}_i\right)}\right\Vert}_{\infty }={M}_{k_i},i=1,2,3,4. \)


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • A. R. Bondarenko
    • 1
  • O. V. Kovalenko
    • 1
  1. 1.Honchar Dnipropetrovs’k National UniversityDniproUkraine

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