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Preservation of Logarithmic Convexity by Positive Operators

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

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

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Authors and Affiliations

  1. St. Petersburg State University, 28, Universitetskii pr., St. Petersburg, 198504, Russia

    O. L. Vinogradov & A. Yu. Ulitskaya

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  1. O. L. Vinogradov
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  2. A. Yu. Ulitskaya
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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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  • DOI: https://doi.org/10.1007/s10958-016-2721-5

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