Journal of Inequalities and Applications (Feb 2020)

Convergence of λ-Bernstein operators based on (p, q)-integers

  • Qing-Bo Cai,
  • Wen-Tao Cheng

DOI
https://doi.org/10.1186/s13660-020-2309-y
Journal volume & issue
Vol. 2020, no. 1
pp. 1 – 17

Abstract

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Abstract In the present paper, we construct a new class of positive linear λ-Bernstein operators based on (p, q)-integers. We obtain a Korovkin type approximation theorem, study the rate of convergence of these operators by using the conception of K-functional and moduli of continuity, and also give a convergence theorem for the Lipschitz continuous functions.

Keywords