Estimates in direct inequalities for the Szász–Mirakyan operator
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2022-12-16
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Springer
Resumen
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.
Descripción
Palabras clave
Szász–Mirakyan operators, Ditzian–Totik modulus of smoothness, Direct inequalities, Steklov means
Citación
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).