Modified Operators Interpolating at Endpoints

Mathematics

Ana Maria Acu¹  Rekha Srivastava²  Ioan Raşa³ 

[1] Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No. 5-7, 550012 Sibiu, Romania;Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada;Department of Mathematics, Technical University of Cluj-Napoca, Str. Memorandumului nr. 28, 400114 Cluj-Napoca, Romania;

关键词: Markov operators;    iterates;    Voronovskaja-type results;    differences of operators;   

DOI  :  10.3390/math9172051

来源: DOAJ

【 摘 要 】

Some classical operators (e.g., Bernstein) preserve the affine functions and consequently interpolate at the endpoints. Other classical operators (e.g., Bernstein–Durrmeyer) have been modified in order to preserve the affine functions. We propose a simpler modification with the effect that the new operators interpolate at endpoints although they do not preserve the affine functions. We investigate the properties of these modified operators and obtain results concerning iterates and their limits, Voronovskaja-type results and estimates of several differences.

【 授权许可】

Unknown