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April 17, 2026Filomat2 citationsOpen Access

Fuzzy approximation theorems via statistical deferred Nörlund Riemann integrability

SMSuresh MahapatraBJBidu JenaSPSusanta Paikray

Key Points

  • The aim is to introduce and explore deferred Nörlund statistical Riemann integrability and summability for fuzzy number-valued functions.
  • Establishing inclusion results between new fuzzy integrability concepts
  • Developing fuzzy Korovkin-type theorems using algebraic test functions
  • Presenting a practical example with a fuzzy linear operator related to Bernstein polynomials
  • Illustrating convergence behaviors graphically using MATLAB
  • New relationships between fuzzy integrability and summability concepts are clarified
  • Fuzzy Korovkin-type theorems are successfully developed
  • The example demonstrates the practical application of fuzzy linear operators in approximating functions
  • Convergence behavior shown graphically, supporting theoretical findings

Abstract

This study introduces and investigates the concepts of deferred N? rlund statistical Riemann integrability and statistical deferred N? rlund Riemann summability for sequences of fuzzy number-valued functions. It begins by establishing an inclusion result that clarifies the relationship between these newly proposed notions. Subsequently, new fuzzy Korovkin-type theorems are developed using the three fun- damental algebraic test functions 1, x, x^2 and based on our proposed means. To demonstrate the practical significance of these results, an example is presented involving a fuzzy positive linear operator associ-ated with Bernstein polynomials. Additionally, the convergence behavior of these operators is illustrated graphically using MATLAB.

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Cite This Study

Mahapatra et al. (2025) studied this question.

synapsesocial.com/papers/69e1cecc5cdc762e9d857d37https://doi.org/10.2298/fil2527609m
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