Some approximation results for the new modification of bernstein-beta operators

Cai Q., Sofyalıoğlu M., Kanat K., ÇEKİM B.

AIMS Mathematics, vol.7, no.2, pp.1831-1844, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.3934/math.2022105
  • Journal Name: AIMS Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.1831-1844
  • Keywords: Korovkin type approximation theorem, modulus of continuity, functions of Lipschitz class, Peetre's K-functionals
  • Ankara Haci Bayram Veli University Affiliated: Yes

Abstract

This paper deals with the newly modification of Beta-type Bernstein operators, preserving constant and Korovkin’s other test functions ei = ti, i = 1, 2 in limit case. Then the uniform convergence of the constructed operators is given. The rate of convergence is obtained in terms of modulus of continuity, Peetre-K functionals and Lipschitz class functions. After that, the Voronovskaya-type asymptotic result for these operators is established. At last, the graphical results of the newly defined operators are discussed.