Uniform convergence of Bernstein–Durrmeyer operators with respect to arbitrary measure

Autor:	Elena E. Berdysheva
Rok vydání:	2012
Předmět:	Discrete mathematics Dominated convergence theorem Pure mathematics Applied Mathematics Normal convergence Uniform convergence Bernstein type operator Measure (mathematics) Convergence tests Uniform absolute-convergence Modes of convergence Analysis Compact convergence Mathematics
Zdroj:	Journal of Mathematical Analysis and Applications. 394:324-336
ISSN:	0022-247X
DOI:	10.1016/j.jmaa.2012.03.004
Popis:	The Bernstein–Durrmeyer operator with respect to arbitrary measure is a modification of the classical Bernstein operator for functions from the corresponding weighted L q -spaces on a simplex in R d . As a first step in studying convergence of this operator, we consider uniform convergence. We prove that uniform convergence holds for all continuous functions if and only if the measure is strictly positive on the simplex. As a consequence, strict positivity of the measure is sufficient for convergence in the weighted L q -spaces.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6e7b320c81d290f22f7496393f9cd010 https://doi.org/10.1016/j.jmaa.2012.03.004 Zobrazit plný text záznamu Full Text from ScienceDirect