  In this article, the approximation properties of the Szasz-Mirakjan type
operators are studied for the function of two variables, and the rate of
convergence of the bivariate operators is determined in terms of total and
partial modulus of continuity. An associated GBS (Generalized Boolean Sum)-form
of the bivariate Szasz-Mirakjan type operators are considered for the function
of two variables to find an approximation of B-continuous and B-differentiable
function in the Bogel's space. Further, the degree of approximation of the GBS
type operators is found in terms of mixed modulus of smoothness and functions
belonging to the Lipschitz class as well as a pioneering result is obtained in
terms of Peetre K-functional. Finally, the rate of convergence of the bivariate
Szasz-Mirakjan type operators and the associated GBS type operators are
examined through graphical representation for the finite and infinite sum which
shows that the rate of convergence of the associated GBS type operators is
better than the bivariate Szasz-Mirakjan type operators.
