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Approximation Properties of Generalized λ-Bernstein–Stancu-Type Operators

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  • Qing-Bo Cai
  • Gülten Torun
  • Ãœlkü Dinlemez Kantar
  • Ding-Xuan Zhou

Abstract

The present study introduces generalized λ-Bernstein–Stancu-type operators with shifted knots. A Korovkin-type approximation theorem is given, and the rate of convergence of these types of operators is obtained for Lipschitz-type functions. Then, a Voronovskaja-type theorem was given for the asymptotic behavior for these operators. Finally, numerical examples and their graphs were given to demonstrate the convergence of Gm,λα,βf,x to fx with respect to m values.

Suggested Citation

  • Qing-Bo Cai & Gülten Torun & Ãœlkü Dinlemez Kantar & Ding-Xuan Zhou, 2021. "Approximation Properties of Generalized λ-Bernstein–Stancu-Type Operators," Journal of Mathematics, Hindawi, vol. 2021, pages 1-17, May.
    • Handle: RePEc:hin:jjmath:5590439
    DOI: 10.1155/2021/5590439
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