Ukrainian Mathematical Journal

, Volume 49, Issue 8, pp 1135–1139 | Cite as

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

  • T. N. Busarova


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.


Monotone Function Exact Estimate Cubature Formula Strict Monotonicity Railway Transport 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. M. Nikol'skii, Quadrature Formulas [in Russian], Nauka, Moscow (1988).Google Scholar
  2. 2.
    J. F. Traub, G. W. Wasilkowski, and H. Wozniakowki, Information, Uncertainty, Complexity, Addison-Wesley, London (1983).MATHGoogle Scholar
  3. 3.
    A. G. Sukharev, Minimax Algorithms in Problems of Numerical Analysis [in Russian], Nauka, Moscow (1989).MATHGoogle Scholar
  4. 4.
    N. P. Korneichuk, “Best cubature formulas for certain classes of functions of many variables,” Mat. Zametki, 3, No. 5, 1416–1437 (1968).MathSciNetGoogle Scholar
  5. 5.
    N. P. Korneichuk, “Optimization of adaptive algorithms for the renewal of monotone functions from the class H ω,” Ukr. Mat. Zh., 45, No. 2, 1627–1634 (1993).MATHCrossRefGoogle Scholar
  6. 6.
    G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, London (1934).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • T. N. Busarova

There are no affiliations available

Personalised recommendations