Statistical Gauge Integrable Functions and Korovkin-Type Approximation Theorems

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发表日期：

2025年6月2日

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Bidu Bhusan Jena,
Susanta Kumar Paikray,
M. Mursaleen

摘要

In this investigation, we introduce and explore the concepts of statistical versions of gauge integrability and gauge summability of sequence of functions under deferred weighted means. Our initial focus involves in establishing foundational limit theorems that interconnect these elegant and potentially valuable concepts. Subsequently, utilizing these techniques we inculcate certain Korovkin-type theorems based on 1, $\nu $ $ν$ and $\nu ^{2}$ $ν^{2}$ functions. Moreover, to demonstrate the effectiveness of our results, we conclude our study with an illustrative example that involves relevant positive linear operators linked to Bernstein polynomials.