On the rates of pointwise convergence for Bernstein polynomials

dc.contributor.author	Adell, José Antonio
dc.contributor.author	Cárdenas-Morales, Daniel
dc.contributor.author	López-Moreno, Antonio Jesús
dc.date.accessioned	2025-04-10T11:40:38Z
dc.date.available	2025-04-10T11:40:38Z
dc.date.issued	2025
dc.description.abstract	Let f be a real bounded function defined on the interval [0, 1], which is affine on a subinterval (a,b) of [0,1], and let Bnf be its associated nth Bernstein polynomial. We prove that, for any x in (a,b), \|Bnf(x)-f(x)\| converges to 0 as n tends to infinity at an exponential rate of decay. Moreover, we show that this property is no longer true at the boundary of (a, b). For Bernstein–Kantorovich type operators similar properties hold, whenever f is assumed to be constant instead of affine.
dc.identifier.issn	1420-9012 (Electronic) 1422-6383 (Print)
dc.identifier.other	doi.org/10.1007/s00025-025-02397-3
dc.identifier.uri	https://hdl.handle.net/10953/4931
dc.language.iso	eng
dc.publisher	Birkhäuser
dc.relation.ispartof	Results in Mathematics
dc.rights.accessRights	info:eu-repo/semantics/openAccess
dc.subject	Bernstein polynomials, locally constant functions, exponential rates, binomial random variable, bernstein-Kantorovich type operators
dc.subject.udc	41A36, 41A10, 41A25, 60E05
dc.title	On the rates of pointwise convergence for Bernstein polynomials
dc.type	info:eu-repo/semantics/article
dc.type.version	info:eu-repo/semantics/publishedVersion