On the Eigenstructure of the Modified Bernstein Operators


GÜREL YILMAZ Ö., Ostrovska S., TURAN M.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, vol.43, no.16, pp.1821-1835, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 16
  • Publication Date: 2022
  • Doi Number: 10.1080/01630563.2022.2136695
  • Journal Name: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Page Numbers: pp.1821-1835
  • Keywords: Bernstein operators, eigenvalues, eigenvectors, modified Bernstein operators, Stirling numbers
  • Recep Tayyip Erdoğan University Affiliated: Yes

Abstract

Starting from the well-known work of Cooper and Waldron published in 2000, the eigenstructure of various Bernstein-type operators has been investigated by many researchers. In this work, the eigenvalues and eigenvectors of the modified Bernstein operators Q(n) have been studied. These operators were introduced by S. N. Bernstein himself, in 1932, for the purpose of accelerating the approximation rate for smooth functions. Here, the explicit formulae for the eigenvalues and corresponding eigenpolynomials together with their limiting behavior are established. The results show that although some outcomes are similar to those for the Bernstein operators, there are essentially different ones as well.