Abstract
AbstractThis 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.
Funder
Ministerio de Ciencia, Innovación y Universidades
Consejería de Economía, Innovación, Ciencia y Empleo, Junta de Andalucía
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis
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