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<p>In this paper, we consider the Mellin–Fejér–Kantorovich type operators under study and outline some of its key properties. In this way, we present a quantitative-type approximation theorem using the polynomial modulus of continuity. Then, we apply the technique developed by Coşkun (Indian J Pure Appl Math 34(3):477–485, 2003), which is based on a weighted Korovkin-type theorem for linear positive operators. Our analysis is carried out in polynomially weighted spaces to establish the weighted uniform convergence of the operators. Also we establish a quantitative estimate by means of the modulus of smoothness and a direct approach result in the for Mellin–Fejér–Kantorovich type operators in the weighted Lebesgue spaces. Finally, we provide specific examples of kernel functions that satisfy the assumptions of the theorems.</p>

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On Some Weighted Approximation Results for Mellin–Fejer–Kantorovich Operators

  • 期刊论文

  • 发表日期：

    2025年9月29日

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  • Başar Yilmaz,
  • Cem Topuz,
  • Ali Aral,
  • Didem Aydin Ari

摘要

In this paper, we consider the Mellin–Fejér–Kantorovich type operators under study and outline some of its key properties. In this way, we present a quantitative-type approximation theorem using the polynomial modulus of continuity. Then, we apply the technique developed by Coşkun (Indian J Pure Appl Math 34(3):477–485, 2003), which is based on a weighted Korovkin-type theorem for linear positive operators. Our analysis is carried out in polynomially weighted spaces to establish the weighted uniform convergence of the operators. Also we establish a quantitative estimate by means of the modulus of smoothness and a direct approach result in the for Mellin–Fejér–Kantorovich type operators in the weighted Lebesgue spaces. Finally, we provide specific examples of kernel functions that satisfy the assumptions of the theorems.