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.