Convergence of \(\lambda \)-Bernstein operators via power series summability method


In this paper we present uniform convergence of a sequence of \(\lambda \) -Bernstein operators via A-statistical convergence and power summability method. A rate of convergence of the sequence of operators are also investigated by means of above mentioned summability methods. The last section is devoted to pointwise convergence (A-statistical convergence) of the sequence of operators in terms of Voronovskaya and Grü ss–Voronovskaya type theorems.

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Braha, N.L., Mansour, T., Mursaleen, M. et al. Convergence of \(\lambda \)-Bernstein operators via power series summability method. J. Appl. Math. Comput. (2020).

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  • A-statistical convergence
  • \(\lambda \)-Bernstein operators
  • Power summability method
  • Korovkin type theorem
  • Voronovskaya type theorem
  • Rate of convergence
  • Grüss–Voronovskaya type theorem

Mathematics Subject Classification

  • 40G10
  • 40C15
  • 41A36
  • 40A35