Bivariate positive linear operators constructed by means of \(q\)-Lagrange polynomials (Q2207635)

Based on multivariable \(q\)-Lagrange polynomials a new positive linear operator is introduced, and its bivariate case is constructed. The order of convergence of the bivariate operators by means of the modulus of continuity and for functions in the Lipschitz class is studied. Further, associated Generalized Boolean Sum operators are defined, and their degree of approximation in terms of the mixed modulus of smoothness for Bögel continuous functions is established. Finally, an \(s\)th order generalization of these operators are given, and the rate of convergence for \(s\)th order continuously differentiable Lipschitz class functions is studied.