On a New Modification of Baskakov Operators with Higher Order of Approximation

Ivan Gadjev, Parvan Parvanov and Rumen Uluchev ()
Additional contact information
Ivan Gadjev: Faculty of Mathematics and Informatics, Sofia University St. Kliment Ohridski, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria
Parvan Parvanov: Faculty of Mathematics and Informatics, Sofia University St. Kliment Ohridski, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria
Rumen Uluchev: Faculty of Mathematics and Informatics, Sofia University St. Kliment Ohridski, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria

Mathematics, 2024, vol. 13, issue 1, 1-18

Abstract: A new Goodman–Sharma-type modification of the Baskakov operator is presented for approximation of bounded and continuous functions on [ 0 , ∞ ) . 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.

Keywords: Baskakov–Durrmeyer operator; Goodman–Sharma operator; non-positive operator; direct theorem; strong converse theorem; K-functional (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/1/64/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/1/64/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2024:i:1:p:64-:d:1554877

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().