Some Statistical and Direct Approximation Properties for a New Form of the Generalization of q-Bernstein Operators with the Parameter λ

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Su L., Kangal E., Kantar Ü., Cai Q.

AXIOMS, vol.13, no.7, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 7
  • Publication Date: 2024
  • Doi Number: 10.3390/axioms13070485
  • Journal Name: AXIOMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Open Archive Collection: AVESIS Open Access Collection
  • Gazi University Affiliated: Yes

Abstract

In this study, a different generalization of q-Bernstein operators with the parameter lambda is an element of [-1,1] is created. The moments and central moments of these operators are calculated, a statistical approximation result for this new type of (lambda,q)-Bernstein operators is obtained, and the convergence properties are analyzed using the Peetre K-functional and the modulus of continuity for this new operator. Finally, a numerical example is given to illustrate the convergence behavior of the newly defined operators.