Modified Operators Interpolating at Endpoints
Date
2021
Authors
Acu, Ana Maria
Raşa, Ioan
Srivastava, Rekha
Journal Title
Journal ISSN
Volume Title
Publisher
Mathematics
Abstract
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.
Description
Keywords
Markov operators, iterates, Voronovskaja-type results, differences of operators
Citation
Acu, A. M., Raşa, I., & Srivastava, R. (2021). Modified Operators Interpolating at Endpoints. Mathematics, 9(17), 1-13. https://doi.org/10.3390/math9172051.