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Preservation of Logarithmic Convexity by Positive Operators

We show that the Szász–Mirakyan and Baskakov operators preserve the logarithmic convexity of functions, whereas the Bernstein and Kantorovich operators do not possess this property.

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References

  1. 1.

    D. V. Anosov, “On the sum of logarithmically convex functions” [in Russian], Mat. Prosvechsh. Ser. 3, No. 5, 158–163 (2001).

  2. 2.

    F. Altomare and M. Campiti, Korovkin-Type Approximation Theory and Its Applications Walter de Gruyter, Berlin etc. (1994).

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Correspondence to O. L. Vinogradov.

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Translated from Problemy Matematicheskogo Analiza 83, December 2015, pp. 41-45.

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Vinogradov, O.L., Ulitskaya, A.Y. Preservation of Logarithmic Convexity by Positive Operators. J Math Sci 213, 504–509 (2016). https://doi.org/10.1007/s10958-016-2721-5

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Keywords

  • Convex Function
  • Positive Root
  • Identity Operator
  • Positive Operator
  • Approximation Theory