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<p>This study addresses a specific problem in fuzzy approximation: classical Korovkin-type theorems often fail when operator sequences show constant noise or oscillations. To fix this, we combine <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((C,1)(E,\mu )\)</EquationSource> </InlineEquation> product summability with statistical convergence. This method lets us find stable limits in sequences that would usually be seen as divergent. We prove a new fuzzy Korovkin-type theorem under this framework and use the fuzzy modulus of continuity to find convergence rates. Our numerical results show that this approach works for cases where the standard Anastassiou–Gal theorem does not, making it a useful option for modeling uncertainty in periodic systems.</p>

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Fuzzy Korovkin Type Theorems for Periodic Continuous Functions via Statistical \((C,1) (E,\mu )\) Product Summability Method

  • 期刊论文

  • 发表日期：

    2026年4月6日

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  • Purshottam Narain Agrawal,
  • Behar Baxhaku

摘要

This study addresses a specific problem in fuzzy approximation: classical Korovkin-type theorems often fail when operator sequences show constant noise or oscillations. To fix this, we combine \((C,1)(E,\mu )\) product summability with statistical convergence. This method lets us find stable limits in sequences that would usually be seen as divergent. We prove a new fuzzy Korovkin-type theorem under this framework and use the fuzzy modulus of continuity to find convergence rates. Our numerical results show that this approach works for cases where the standard Anastassiou–Gal theorem does not, making it a useful option for modeling uncertainty in periodic systems.