Bivariate positive linear operators constructed by means of q-Lagrange polynomials

Abstract In this paper we propose an extension of the linear positive operators constructed by means of the q-Lagrange polynomials and investigate the order of convergence by means of the complete and partial moduli of continuity and the Peetre's K-functional. We also define the associated Generalized Boolean Sum(GBS) operators and investigate the rate of convergence of these operators with the aid of mixed modulus of smoothness for Bogel continuous and Bogel differentiable functions. Finally, we introduce an sth (s being a non-negative integer) order generalization of the above operators and study the degree of approximation of these operators for sth order continuously differentiable Lipschitz class functions.