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<p>In this article, we consider Kantorovich and Durrmeyer-type extensions of the discrete operators defined by İçöz et al. [Filomat 30 (2) (2016), 429–440], which are associated with Miller–Lee polynomials. The primary focus of our study is to obtain the complete asymptotic expansions for these operators. For this purpose, we derive explicit expressions for their moments and central moments in terms of Stirling numbers. Additionally, we examine their convergence behavior, derive quantitative Voronovskaya-type estimates, and establish weighted approximation results. The theoretical results are validated through graphical illustrations and numerical tables.</p>

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Complete asymptotic expansion for operators associated with Miller–Lee polynomials

  • 期刊论文

  • 发表日期：

    2026年7月23日

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  • Deepak Malik,
  • Vijay Gupta,
  • Vaibhav Sharma

摘要

In this article, we consider Kantorovich and Durrmeyer-type extensions of the discrete operators defined by İçöz et al. [Filomat 30 (2) (2016), 429–440], which are associated with Miller–Lee polynomials. The primary focus of our study is to obtain the complete asymptotic expansions for these operators. For this purpose, we derive explicit expressions for their moments and central moments in terms of Stirling numbers. Additionally, we examine their convergence behavior, derive quantitative Voronovskaya-type estimates, and establish weighted approximation results. The theoretical results are validated through graphical illustrations and numerical tables.