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<p>In this paper, we address the problem of extending Korovkin-type approximation theorems to sequences of monotone and sublinear operators via the concept of power series statistical convergence (statistical convergence with respect to power series methods), which is incompatible with statistical convergence and in general a non-matrix method. It is important to emphasise that any positive linear operator is monotone sublinear, but the opposite is not correct. We establish several Korovkin-type theorems under these generalized settings and demonstrate their applicability with concrete examples.</p>

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Approximation theorems via power series statistical convergence and applications for sequences of monotone and sublinear operators

  • 期刊论文

  • 发表日期：

    2025年7月26日

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  • Sevda Yıldız,
  • Kamil Demirci,
  • Fadime Dirik

摘要

In this paper, we address the problem of extending Korovkin-type approximation theorems to sequences of monotone and sublinear operators via the concept of power series statistical convergence (statistical convergence with respect to power series methods), which is incompatible with statistical convergence and in general a non-matrix method. It is important to emphasise that any positive linear operator is monotone sublinear, but the opposite is not correct. We establish several Korovkin-type theorems under these generalized settings and demonstrate their applicability with concrete examples.