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<p>This paper focuses on exploring various concepts related to statistical convergence, including statistical convergence almost everywhere, statistical convergence almost uniformly, and different forms of statistical integrability such as statistical Lebesgue integrable, statistical Lebesgue integrable almost everywhere, and statistical Lebesgue integrable almost uniformly, all within the framework of deferred weighted summability means. We begin by presenting several foundational theorems, accompanied by examples, and apply these above notions to the measure-theoretic version of the Korovkin-type approximation theorems, using three trigonometric test functions 1, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\cos \nu \)</EquationSource> </InlineEquation>, and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\sin \nu \)</EquationSource> </InlineEquation>, with our proposed summability means. Throughout the paper, we also include several graphical representations generated with MATLAB software to visually support the newly introduced concepts and to demonstrate the convergence and integrability behavior of the operators.</p>

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An Innovative Framework for Summability Methods in Measure-Theoretic Approximation

  • 期刊论文

  • 发表日期：

    2026年5月30日

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  • Priyadarsini Parida,
  • Bidu Bhusan Jena,
  • Susanta Kumar Paikray

摘要

This paper focuses on exploring various concepts related to statistical convergence, including statistical convergence almost everywhere, statistical convergence almost uniformly, and different forms of statistical integrability such as statistical Lebesgue integrable, statistical Lebesgue integrable almost everywhere, and statistical Lebesgue integrable almost uniformly, all within the framework of deferred weighted summability means. We begin by presenting several foundational theorems, accompanied by examples, and apply these above notions to the measure-theoretic version of the Korovkin-type approximation theorems, using three trigonometric test functions 1, \(\cos \nu \) , and \(\sin \nu \) , with our proposed summability means. Throughout the paper, we also include several graphical representations generated with MATLAB software to visually support the newly introduced concepts and to demonstrate the convergence and integrability behavior of the operators.