On Fuzzy Approximation Theorems for Functions of Two Variables via Statistical Deferred N\"{o}rlund Summability

Document Type : Research Paper

Authors

1 Department of Mathematics, Kuntala Kumari Sabat Women's College, Balasore 756003, Odisha, India

2 Faculty of Science (Mathematics), Sri Sri University, Cuttack 754006, Odisha, India

3 Department of Mathematics, Veer Surendra Sai University of Technology, Burla 768018, Odisha, India

4 Department of Mathematical Sciences, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, Tamilnadu, India

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 double sequences of fuzzy number-valued functions of two variables. An inclusion result is first established to clarify the relationship between these newly proposed notions in the bivariate setting. Building on this framework, new fuzzy Korovkin-type approximation theorems are developed using the four fundamental algebraic test functions $1$, $x$, $y$ and $x^{2}+y^{2}$ under the proposed means. To highlight the applicability of the results, an example is provided involving a fuzzy positive linear operator associated with bivariate Bernstein polynomials. Furthermore, the convergence behavior of these operators is illustrated graphically with the aid of MATLAB.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 23, Issue 2
March and April 2026
Pages 17-35

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