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