In this study, we give some approximation results for the tensor product of
(p,q)-Bal?zs-Szabados operators associated generalized Boolean sum (GBS)
operators. Firstly, we introduce tensor product (p,q)-Bal?zs-Szabados
operators and give an uniform convergence theorem of these operators on
compact rectangular regions with an illustrative example. Then we estimate
the approximation for the tensor product (p,q)-Bal?zs-Szabados operators in
terms of the complete modulus of continuity, the partial modulus of
continuity, Lipschitz functions and Petree?s K-functional corresponding to
the second modulus of continuity. After that, we introduce the GBS operators
associated the tensor product (p,q)-Bal?zs-Szabados operators. Finally, we
improve the rate of smoothness by the mixed modulus of smoothness and
Lipschitz class of B?gel continuous functions for the GBS operators.