On the eigenstructure of the (alpha, q)-Bernstein operator

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Koroglu B., TAŞDELEN YEŞİLDAL F.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.50, no.4, pp.1111-1122, 2021 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.15672/hujms.779544
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1111-1122
  • Keywords: calculus, (alpha, q)-Bernstein polynomials, eigenvalues, eigenvectors, BERNSTEIN POLYNOMIALS
  • Ankara University Affiliated: Yes

Abstract

The eigenvalues and eigenvectors of (alpha, q)-Bernstein operators are unknown and not studied in the literature. As the main result of this article, the eigenvalues and eigenvectors of (alpha, q)-Bernstein operators are obtained. Moreover, we will give the asymptotic behaviour of these eigenvalues and eigenvectors for all q > 0. Some eigenvectors for various values of alpha and q are depicted.