Adell, José A.Cárdenas-Morales, Daniel2024-01-312024-01-312022-12-16Adell, 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).1578-7303 (print) 1579-1505 (electronic)10.1007/s13398-022-01379-2https://hdl.handle.net/10953/1859This 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.engAtribución-NoComercial-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nc-nd/3.0/es/Szász–Mirakyan operatorsDitzian–Totik modulus of smoothnessDirect inequalitiesSteklov meansinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess