Journal of Inequalities and Applications (Mar 2018)

Approximation properties of λ-Bernstein operators

  • Qing-Bo Cai,
  • Bo-Yong Lian,
  • Guorong Zhou

DOI
https://doi.org/10.1186/s13660-018-1653-7
Journal volume & issue
Vol. 2018, no. 1
pp. 1 – 11

Abstract

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Abstract In this paper, we introduce a new type λ-Bernstein operators with parameter λ∈[−1,1] $\lambda\in[-1,1]$, we investigate a Korovkin type approximation theorem, establish a local approximation theorem, give a convergence theorem for the Lipschitz continuous functions, we also obtain a Voronovskaja-type asymptotic formula. Finally, we give some graphs and numerical examples to show the convergence of Bn,λ(f;x) $B_{n,\lambda }(f;x)$ to f(x) $f(x)$, and we see that in some cases the errors are smaller than Bn(f) $B_{n}(f)$ to f.

Keywords