Fuzzy Approximation Theorems via Statistical Deferred N\"{o}rlund Riemann Integrability

Abstract

This study introduces and investigates the concepts of deferred N\"{o}rlund statistical Riemann integrability and statistical deferred N\"{o}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 three fundamental algebraic test functions: $1$, $x$ and $x^{2}$. To demonstrate the practical significance of these results, an example is presented involving a fuzzy positive linear operator associated with Bernstein polynomials. Additionally, the convergence behavior of these operators is illustrated graphically using MATLAB.