Approximation by modified Durrmeyer type Jakimovski-Leviatan operators

Cai Q., GÜNGÖR Ş. Y., ÇEKİM B., Özarslan M. A.

Applied Mathematics, vol.40, no.3, pp.709-724, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 3
  • Publication Date: 2025
  • Doi Number: 10.1007/s11766-025-5326-2
  • Journal Name: Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.709-724
  • Keywords: 41A10, 41A35, 41A36, Appell polynomials, Durrmeyer operators, Jakimovski-Leviatan operators, Lipschitz type function space, modulus of continuity
  • Gazi University Affiliated: Yes

Abstract

In the present paper, the modified Durrmeyer type Jakimovski-Leviatan operators are presented and their approximation properties are examined. It has shown that the new operators are the Gamma transform of the Jakimovski-Leviatan operators. The degree of approximation is given by the modulus of continuity. It has been stressed that, there are other operators having the same error estimation with the operators, arising from the Szász-Durrmeyer operators. Then the degree of global approximation is obtained in a special Lipschitz type function space. Further, a Voronovskaja type asymptotic formula and Grüss-Voronovskaja type theorem are given. The approximation with these operators is visualized with the help of error tables and graphical examples.