A note on the remainder in the approximation of functions by some positive linear operators

In this note we give representations for the remainder in approximations formulas generated by positive linear operators which preserve some functions including linear functions. We show that in these cases the Peano kernel from the integral representation of the remainder has the same sign on the d...

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Bibliographic Details
Published in:Positivity : an international journal devoted to the theory and applications of positivity in analysis Vol. 27; no. 5; p. 61
Main Author: Birou, Marius-Mihai
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.11.2023
Springer Nature B.V
Subjects:
Approximation
Calculus of Variations and Optimal Control; Optimization
Econometrics
Fourier Analysis
Linear functions
Linear operators
Mathematics
Mathematics and Statistics
Operator Theory
Operators (mathematics)
Potential Theory
Quadratures
Representations
Quadrature
41A55
41A36
41A25
41A80
Positive linear operator
Remainder term
Peano kernel
Iterates
ISSN:1385-1292, 1572-9281
Online Access:Get full text
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Summary:In this note we give representations for the remainder in approximations formulas generated by positive linear operators which preserve some functions including linear functions. We show that in these cases the Peano kernel from the integral representation of the remainder has the same sign on the definition domain. Applications to the iterates of some positive linear operators and quadrature formulas are given.
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ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-023-01014-3