This article deals with the approximation properties of the bivariate operators which are the combination of Bernstein-Chlodowsky operators and the Szász operators involving Appell polynomials. We investigate the degree of approximation of the operators with the help of the complete modulus of continuity and the partial moduli of continuity. In the last section of the paper, we introduce the generalized Boolean sum (GBS) of these bivariate Chlodowsky-Szasz-Appell-type operators and examine the order of approximation in the Bögel space of continuous functions by means of the mixed modulus of smoothness.
Bǎrbosu and Muraru (2015) introduced the bivariate generalization of the q-Bernstein-Schurer-Stancu operators and constructed a GBS operator of q-Bernstein-Schurer-Stancu type. The concern of this paper is to obtain the rate of convergence in terms of the partial and complete modulus of continuity and the degree of approximation by means of Lipschitz-type class for the bivariate operators. In the last section we estimate the degree of approximation by means of Lipschitz class function and the rate of convergence with the help of mixed modulus of smoothness for the GBS operator of q-Bernstein-Schurer-Stancu type. Furthermore, we show comparisons by some illustrative graphics in Maple for the convergence of the operators to some functions.
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