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Parida, Priyadarsini, Jena, Bidu Bhusan, Paikray, Susanta Kumar, Mursaleen, M.. (1405). On Fuzzy Approximation Theorems for Functions of Two Variables via Statistical Deferred N\"{o}rlund Summability. نشریه علمی دانشگاه سیستان و بلوچستان, 23(2), 17-35. doi: 10.22111/ijfs.2026.53142.9401
Priyadarsini Parida; Bidu Bhusan Jena; Susanta Kumar Paikray; M. Mursaleen. "On Fuzzy Approximation Theorems for Functions of Two Variables via Statistical Deferred N\"{o}rlund Summability". نشریه علمی دانشگاه سیستان و بلوچستان, 23, 2, 1405, 17-35. doi: 10.22111/ijfs.2026.53142.9401
Parida, Priyadarsini, Jena, Bidu Bhusan, Paikray, Susanta Kumar, Mursaleen, M.. (1405). 'On Fuzzy Approximation Theorems for Functions of Two Variables via Statistical Deferred N\"{o}rlund Summability', نشریه علمی دانشگاه سیستان و بلوچستان, 23(2), pp. 17-35. doi: 10.22111/ijfs.2026.53142.9401
Parida, Priyadarsini, Jena, Bidu Bhusan, Paikray, Susanta Kumar, Mursaleen, M.. On Fuzzy Approximation Theorems for Functions of Two Variables via Statistical Deferred N\"{o}rlund Summability. نشریه علمی دانشگاه سیستان و بلوچستان, 1405; 23(2): 17-35. doi: 10.22111/ijfs.2026.53142.9401

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

Iranian Journal of Fuzzy Systems
دوره 23، شماره 2، خرداد و تیر 2026، صفحه 17-35    اصل مقاله (21.76 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2026.53142.9401
نویسندگان
Priyadarsini Parida1؛ Bidu Bhusan Jena* 2؛ Susanta Kumar Paikray3؛ M. Mursaleen4
1Department of Mathematics, Kuntala Kumari Sabat Women's College, Balasore 756003, Odisha, India
2Faculty of Science (Mathematics), Sri Sri University, Cuttack 754006, Odisha, India
3Department of Mathematics, Veer Surendra Sai University of Technology, Burla 768018, Odisha, India
4Department of Mathematical Sciences, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, Tamilnadu, India
چکیده
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.
کلیدواژه‌ها
Double sequence of Fuzzy number-valued functions؛ Double Riemann integrals؛ Deferred N\"{o}rlund mean؛ Bivariate Bernstein polynomials؛ Korovkin-type theorems
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