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<p>In this note, we introduce a multivariate power series technique to test the statistical convergence of multiple sequences. Our primary goal is to establish a new multivariate Korovkin-type theorem based on this convergence approach. We also analyze the rate of convergence for the associated positive linear operators. Additionally, we extend some existing Korovkin-type results from (Boyanov and Veselinov in Bull. Math. Soc. Sci. Math. Roum. 14(62)(1):9–13, <CitationRef CitationID="CR4">1970</CitationRef>) and (Demirci and Dirik in Bull. Korean Math. Soc. 47(4):825–837, <CitationRef CitationID="CR11">2010</CitationRef>) using the proposed method. Further, we provide some illustrative examples that demonstrate the validity and applicability of the proposed theorems.</p>

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Some Korovkin-type theorems using multivariate power series technique

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  • 发表日期：

    2025年7月4日

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  • Mrutyunjaya Meher,
  • Prasanta Kumar Ray

摘要

In this note, we introduce a multivariate power series technique to test the statistical convergence of multiple sequences. Our primary goal is to establish a new multivariate Korovkin-type theorem based on this convergence approach. We also analyze the rate of convergence for the associated positive linear operators. Additionally, we extend some existing Korovkin-type results from (Boyanov and Veselinov in Bull. Math. Soc. Sci. Math. Roum. 14(62)(1):9–13, 1970) and (Demirci and Dirik in Bull. Korean Math. Soc. 47(4):825–837, 2010) using the proposed method. Further, we provide some illustrative examples that demonstrate the validity and applicability of the proposed theorems.