Generalized Weighted Statistical Convergence for Double Sequences of Fuzzy Numbers and Associated Korovkin-Type Approximation Theorem

We define the notions of weighted (lambda, mu)-statistical convergence of order (gamma(1), gamma(2)) and strongly weighted (lambda, mu)-summability of (gamma(1), gamma(2)) or fuzzy double sequences, where 0 < gamma(1), gamma(2) <= 1. We establish an inclusion result and a theorem presenting a connection between these concepts. Moreover, we apply our new concept of weighted (lambda, mu)-statistical convergence of order (gamma(1), gamma(2)) to prove Korovkin-type approximation theorem for functions of two variables in a fuzzy sense. Finally, an illustrative example is provided with the help of q-analogue of fuzzy Bernstein operators for bivariate functions which shows the significance of our approximation theorem.