Resumen: This paper deals with the approximation of functions by the classical Bernstein polynomials in terms of the Ditzian–Totik modulus of smoothness. Asymptotic and non-asymptotic results are respectively stated for continuous and twice continuously differentiable functions. By using a probabilistic approach, known results are either completed or strengthened. Idioma: Inglés DOI: 10.1007/s00025-022-01680-x Año: 2022 Publicado en: Results in Mathematics 77, 4 (2022), 166 [13 pp.] ISSN: 1422-6383 Factor impacto JCR: 2.2 (2022) Categ. JCR: MATHEMATICS, APPLIED rank: 49 / 267 = 0.184 (2022) - Q1 - T1 Categ. JCR: MATHEMATICS rank: 27 / 329 = 0.082 (2022) - Q1 - T1 Factor impacto CITESCORE: 1.8 - Mathematics (Q3)