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<p>In this article, we capture a new Durrmeyer type operator, linking adjoint Bernoulli polynomials with the Baskakov basis functions. We estimate its moments and central moments and provide approximation results which include Korovkin-type estimate in weighted space. Additionally, we present a graphical interpretation of the operators applied to certain functions, quantitative Voronovskaja’s theorem in weighted space, and a theorem involving Peetre’s K-functional. Furthermore, we give theorems based on difference of operators.</p>

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On Durrmeyer Type Operator Linking Bernoulli Polynomials

  • 期刊论文

  • 发表日期：

    2025年4月17日

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  • Deepak Malik,
  • Vijay Gupta

摘要

In this article, we capture a new Durrmeyer type operator, linking adjoint Bernoulli polynomials with the Baskakov basis functions. We estimate its moments and central moments and provide approximation results which include Korovkin-type estimate in weighted space. Additionally, we present a graphical interpretation of the operators applied to certain functions, quantitative Voronovskaja’s theorem in weighted space, and a theorem involving Peetre’s K-functional. Furthermore, we give theorems based on difference of operators.