Skip to main content
SpringerLink
Log in

Monotonicity conditions for a sequence of generalized polynomials of S. N. Bernshtein and A. O. Gel'fond

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

Abstract

It is shown that the sequence of generalized polynomials of S. N. Bernshtein and A. O. Gel'fond, which corresponds to a functionf(x), is an increasing or decreasing sequence depending on the concavity or convexity of the function. Analogous results are given in the case of functions of two variables.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. O. Aramá, “Proprietati privind monotonia siului polinoamelor de interpolare alelui S. N. Bernstein si aplicarea lor la studiul apraximarii functililor,” Acad. Romania Fil. Cluj Studii, Cere Mat.,8, No. 3–4, 195–210 (1957).

    Google Scholar 

  2. A. Lopas, “Some properties of the linear positive operators,” Matematica (Cluj),9 (32), No. 1, 77–83 (1967).

    Google Scholar 

  3. A. O. Gel'fond, Calculus of Finite Differences [in Russian], Moscow (1960).

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Academy of Sciences of the Azerbaidzhan SSR, USSR

    V. M. Shakhverdiev

Authors
  1. V. M. Shakhverdiev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 5, No. 6, pp. 747–752, June, 1969.

In conclusion, the author wishes to express his thanks to I. I. Ibragimov and A. D. Gadzhiev for their interest in his work.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shakhverdiev, V.M. Monotonicity conditions for a sequence of generalized polynomials of S. N. Bernshtein and A. O. Gel'fond. Mathematical Notes of the Academy of Sciences of the USSR 5, 446–449 (1969). https://doi.org/10.1007/BF01374475

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01374475

Keywords

Search

Navigation