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The Korovkin theorem (Korovkin, Linear Operators and Approximation Theory. Hindustan Publishing Corporation, Delhi, 1960) has significant importance within the field of approximation theory and has spawned numerous generalizations. Among these, nonlinear extensions of the Korovkin theorem stand out as particularly noteworthy. In the chapter, we present Korovkin-type theorems for nonlinear operators using the power series summability method. Additionally, we provide an example demonstrating that our results are more general than the classical ones.

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Some Results of Korovkin Type For Nonlinear Operators

  • 会议论文

  • 发表日期：

    2026年

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  • Emre Taş,
  • Sevil Aykanat

摘要

The Korovkin theorem (Korovkin, Linear Operators and Approximation Theory. Hindustan Publishing Corporation, Delhi, 1960) has significant importance within the field of approximation theory and has spawned numerous generalizations. Among these, nonlinear extensions of the Korovkin theorem stand out as particularly noteworthy. In the chapter, we present Korovkin-type theorems for nonlinear operators using the power series summability method. Additionally, we provide an example demonstrating that our results are more general than the classical ones.