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<p>We introduce a positive linear operator acting on the Banach space of all continuous functions on the unit interval via the Moran model studied in population genetics. We show that this operator, named the Moran operator, uniformly approximates every continuous function on the unit interval. Furthermore, some limit theorems for the iterates of the Moran operator are obtained.</p>

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On Some Properties of a Positive Linear Operator via the Moran Model in Population Genetics

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Takahiro Aoyama,
  • Ryuya Namba

摘要

We introduce a positive linear operator acting on the Banach space of all continuous functions on the unit interval via the Moran model studied in population genetics. We show that this operator, named the Moran operator, uniformly approximates every continuous function on the unit interval. Furthermore, some limit theorems for the iterates of the Moran operator are obtained.