Difference of Some Positive Linear Approximation Operators for Higher-Order Derivatives

Date

2020

Authors

Gupta, Vijay
Acu, Ana Maria
Srivastava, H.M.

Journal Title

Journal ISSN

Volume Title

Publisher

Symmetry

Abstract

In the present paper, we deal with some general estimates for the difference of operators which are associated with different fundamental functions. In order to exemplify the theoretical results presented in (for example) Theorem 2, we provide the estimates of the differences between some of the most representative operators used in Approximation Theory in especially the difference between the Baskakov and the Szász–Mirakyan operators, the difference between the Baskakov and the Szász–Mirakyan–Baskakov operators, the difference of two genuine-Durrmeyer type operators, and the difference of the Durrmeyer operators and the Lupaş–Durrmeyer operators. By means of illustrative numerical examples, we show that, for particular cases, our result improves the estimates obtained by using the classical result of Shisha and Mond. We also provide the symmetry aspects of some of these approximations operators which we have studied in this paper.

Description

Keywords

approximation operators, differences of operators, Szász–Mirakyan–Baskakov operators, Durrmeyer type operators, Bernstein polynomials, modulus of continuity

Citation

Gupta, V.; Acu, A. M.; & Srivastava, H. M. (2020). Difference of some positive linear approximation operators for higher-order derivatives. Symmetry, 12(6), DOI: 10.3390/sym12060915