On fuzzy approximation theorems for functions of two variables via statistical deferred Norlund summability

Abstract

This study introduces and investigates the concepts of deferred No & uml;rlund statistical Riemann integrability and statistical deferred No & uml;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 x2+y2 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.