Approximation of Real Functions by a Generalization of Ismail–May Operator

Adrian Holhoş
Additional contact information
Adrian Holhoş: Department of Mathematics, Technical University of Cluj-Napoca, Str. Memorandumului 28, RO-400114 Cluj-Napoca, Romania

Mathematics, 2022, vol. 10, issue 10, 1-13

Abstract: In this paper, we generalize a sequence of positive linear operators introduced by Ismail and May and we study some of their approximation properties for different classes of continuous functions. First, we estimate the error of approximation in terms of the usual modulus of continuity and the second-order modulus of Ditzian and Totik. Then, we characterize the bounded functions that can be approximated uniformly by these new operators. In the last section, we obtain the most important results of the paper. We give the complete asymptotic expansion for the operators and we deduce a Voronovskaya-type theorem, results that hold true for smooth functions with exponential growth.

Keywords: positive linear operators; Ismail–May operators; Jain operators; moduli of continuity; asymptotic expansion; Voronovskaya-type theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/10/1650/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/10/1650/ (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:10:y:2022:i:10:p:1650-:d:813915

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 ().