Use of identity of A. Hurwitz for construction of a linear positive operator of approximation
By using a general algebraic identity of Adolf Hurwitz [1], which generalizes an important identity of Abel, we construct a new operator \(S_m^{(\beta_1,\ldots,\beta_m)}\) approximating the functions. A special case of this is the operator \(Q_m^\beta\) of Cheney-Sharma. We show that this new opera...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Publishing House of the Romanian Academy
2002-02-01
|
| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/714 |
| Summary: | By using a general algebraic identity of Adolf Hurwitz [1], which generalizes an important identity of Abel, we construct a new operator \(S_m^{(\beta_1,\ldots,\beta_m)}\) approximating the functions.
A special case of this is the operator \(Q_m^\beta\) of Cheney-Sharma.
We show that this new operator, applied to a function \(f\in C[0,1]\), is interpolatory at both sides of the interval \([0,1]\), and reproduces the linear functions.
We also give an integral representation of the remainder of the approximation formula of the function \(f\) by means of this operator. By applying a criterion of T. Popoviciu [2], is also given an expression of this remainder by means of divided
difference of second order. |
|---|---|
| ISSN: | 2457-6794 2501-059X |