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The basic aim of this work is to prove the approximation problem for a sequence of positive linear operators (PLOs) acting from \(H_{\omega }\left ( D\right ) \) to \(C_{b}\left ( D\right ) \) where \(D=\left [ 0,\infty \right ) \) by means of the notion of \(\mathcal {I}\) -statistical uniform convergence. Next, an example will be given where our new approximation theorem works but some of the previous results do not. Also, the rate of \(\mathcal {I}\) -statistical uniform convergence for the sequences of PLOs is computed by way of the modulus of smoothness.

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Korovkin-type Approximation Theorems for Functions with the Help of \(\mathcal {I}\) -statistical Convergence

  • 会议论文

  • 发表日期：

    2026年

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  • Fadime Dirik,
  • Kamil Demirci,
  • Sevda Yıldız

摘要

The basic aim of this work is to prove the approximation problem for a sequence of positive linear operators (PLOs) acting from \(H_{\omega }\left ( D\right ) \) to \(C_{b}\left ( D\right ) \) where \(D=\left [ 0,\infty \right ) \) by means of the notion of \(\mathcal {I}\) -statistical uniform convergence. Next, an example will be given where our new approximation theorem works but some of the previous results do not. Also, the rate of \(\mathcal {I}\) -statistical uniform convergence for the sequences of PLOs is computed by way of the modulus of smoothness.