On a New Modification of Baskakov Operators with Higher Order of Approximation
A new Goodman–Sharma-type modification of the Baskakov operator is presented for approximation of bounded and continuous functions on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo>&...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/1/64 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841549123109519360 |
|---|---|
| author | Ivan Gadjev Parvan Parvanov Rumen Uluchev |
| author_facet | Ivan Gadjev Parvan Parvanov Rumen Uluchev |
| author_sort | Ivan Gadjev |
| collection | DOAJ |
| description | A new Goodman–Sharma-type modification of the Baskakov operator is presented for approximation of bounded and continuous functions on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mspace width="0.166667em"></mspace><mo>∞</mo><mo>)</mo></mrow></semantics></math></inline-formula>. We study the approximation error of the proposed operator. Our main results are a direct theorem and strong converse theorem with respect to a related K-functional. Both theorems give complete characterization of the uniform approximation error in means of the K-functional. The new operator suggested by the authors is linear but non-positive. However, it has the advantage of a higher order of approximation compared to the Goodman–Sharma variant of the Baskakov operator defined in 2005 by Finta. The results of computational simulations are given. |
| format | Article |
| id | doaj-art-1ed403cbfc4c49efb371af0a1682adc4 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-1ed403cbfc4c49efb371af0a1682adc42025-01-10T13:18:08ZengMDPI AGMathematics2227-73902024-12-011316410.3390/math13010064On a New Modification of Baskakov Operators with Higher Order of ApproximationIvan Gadjev0Parvan Parvanov1Rumen Uluchev2Faculty of Mathematics and Informatics, Sofia University St. Kliment Ohridski, 5 James Bourchier Blvd., 1164 Sofia, BulgariaFaculty of Mathematics and Informatics, Sofia University St. Kliment Ohridski, 5 James Bourchier Blvd., 1164 Sofia, BulgariaFaculty of Mathematics and Informatics, Sofia University St. Kliment Ohridski, 5 James Bourchier Blvd., 1164 Sofia, BulgariaA new Goodman–Sharma-type modification of the Baskakov operator is presented for approximation of bounded and continuous functions on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mspace width="0.166667em"></mspace><mo>∞</mo><mo>)</mo></mrow></semantics></math></inline-formula>. We study the approximation error of the proposed operator. Our main results are a direct theorem and strong converse theorem with respect to a related K-functional. Both theorems give complete characterization of the uniform approximation error in means of the K-functional. The new operator suggested by the authors is linear but non-positive. However, it has the advantage of a higher order of approximation compared to the Goodman–Sharma variant of the Baskakov operator defined in 2005 by Finta. The results of computational simulations are given.https://www.mdpi.com/2227-7390/13/1/64Baskakov–Durrmeyer operatorGoodman–Sharma operatornon-positive operatordirect theoremstrong converse theoremK-functional |
| spellingShingle | Ivan Gadjev Parvan Parvanov Rumen Uluchev On a New Modification of Baskakov Operators with Higher Order of Approximation Mathematics Baskakov–Durrmeyer operator Goodman–Sharma operator non-positive operator direct theorem strong converse theorem K-functional |
| title | On a New Modification of Baskakov Operators with Higher Order of Approximation |
| title_full | On a New Modification of Baskakov Operators with Higher Order of Approximation |
| title_fullStr | On a New Modification of Baskakov Operators with Higher Order of Approximation |
| title_full_unstemmed | On a New Modification of Baskakov Operators with Higher Order of Approximation |
| title_short | On a New Modification of Baskakov Operators with Higher Order of Approximation |
| title_sort | on a new modification of baskakov operators with higher order of approximation |
| topic | Baskakov–Durrmeyer operator Goodman–Sharma operator non-positive operator direct theorem strong converse theorem K-functional |
| url | https://www.mdpi.com/2227-7390/13/1/64 |
| work_keys_str_mv | AT ivangadjev onanewmodificationofbaskakovoperatorswithhigherorderofapproximation AT parvanparvanov onanewmodificationofbaskakovoperatorswithhigherorderofapproximation AT rumenuluchev onanewmodificationofbaskakovoperatorswithhigherorderofapproximation |