Linear Approximation Processes Based on Binomial Polynomials
The purpose of the article is to highlight the role of binomial polynomials in the construction of classes of positive linear approximation sequences on Banach spaces. Our results aim to introduce and study an integral extension in Kantorovich sense of these binomial operators, which are useful in a...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-07-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/15/2413 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | The purpose of the article is to highlight the role of binomial polynomials in the construction of classes of positive linear approximation sequences on Banach spaces. Our results aim to introduce and study an integral extension in Kantorovich sense of these binomial operators, which are useful in approximating signals in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mi>p</mi></msub><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula> spaces, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>≥</mo><mn>1</mn></mrow></semantics></math></inline-formula>. Also, inspired by the coincidence index that appears in the definition of entropy, a general class of discrete operators related to the squared fundamental basis functions is under study. The fundamental tools used in error evaluation are the smoothness moduli and Peetre’s K-functionals. In a distinct section, numerical applications are presented and analyzed. |
|---|---|
| ISSN: | 2227-7390 |