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Title: Estimates in direct inequalities for the Szász–Mirakyan operator
Authors: Adell, José A.
Cárdenas-Morales, Daniel
Abstract: This paper deals with the approximation of continuous functions by the classical Szász– Mirakyan operator. We give new bounds for the constant in front of the second order Ditzian–Totik modulus of smoothness in direct inequalities. Asymptotic and non asymptotic results are stated. We use both analytical and probabilistic methods, the latter involving the representation of the operators in terms of the standard Poisson process. A smoothing technique based on a modification of the Steklov means is also applied.
Keywords: Szász–Mirakyan operators
Ditzian–Totik modulus of smoothness
Direct inequalities
Steklov means
Issue Date: 16-Dec-2022
metadata.dc.description.sponsorship: Universidad de Jaén/CBUA. This work is partially supported by the Spanish government Research Project PGC2018-097621-B-I00. The second author is also supported by Junta de Andalucía Research Group FQM-0178.
Publisher: Springer
Citation: Adell, J.A., Cárdenas-Morales, D. Estimates in direct inequalities for the Szász–Mirakyan operator. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 43 (2023).
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