000124042 001__ 124042 000124042 005__ 20241125101130.0 000124042 0247_ $$2doi$$a10.1007/s13398-022-01379-2 000124042 0248_ $$2sideral$$a132605 000124042 037__ $$aART-2023-132605 000124042 041__ $$aeng 000124042 100__ $$0(orcid)0000-0001-8331-5160$$aAdell, José A.$$uUniversidad de Zaragoza 000124042 245__ $$aEstimates in direct inequalities for the Szász–Mirakyan operator 000124042 260__ $$c2023 000124042 5060_ $$aAccess copy available to the general public$$fUnrestricted 000124042 5203_ $$aThis 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. 000124042 536__ $$9info:eu-repo/grantAgreement/ES/MCIU/PGC2018-097621-B-I00 000124042 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000124042 590__ $$a1.8$$b2023 000124042 592__ $$a0.906$$b2023 000124042 591__ $$aMATHEMATICS$$b39 / 490 = 0.08$$c2023$$dQ1$$eT1 000124042 593__ $$aAlgebra and Number Theory$$c2023$$dQ1 000124042 593__ $$aAnalysis$$c2023$$dQ1 000124042 593__ $$aGeometry and Topology$$c2023$$dQ1 000124042 593__ $$aApplied Mathematics$$c2023$$dQ1 000124042 593__ $$aComputational Mathematics$$c2023$$dQ2 000124042 594__ $$a4.7$$b2023 000124042 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000124042 700__ $$aCárdenas Morales, Daniel 000124042 7102_ $$12007$$2265$$aUniversidad de Zaragoza$$bDpto. Métodos Estadísticos$$cÁrea Estadís. Investig. Opera. 000124042 773__ $$g117 (2023), 43 [12 pp]$$pRev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat.$$tRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas$$x1578-7303 000124042 8564_ $$s287634$$uhttps://zaguan.unizar.es/record/124042/files/texto_completo.pdf$$yVersión publicada 000124042 8564_ $$s1042762$$uhttps://zaguan.unizar.es/record/124042/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000124042 909CO $$ooai:zaguan.unizar.es:124042$$particulos$$pdriver 000124042 951__ $$a2024-11-22-11:58:43 000124042 980__ $$aARTICLE