In this article, we establish an extension of the bivariate generalization of the -Bernstein type operators involving parameter and extension of GBS (Generalized Boolean Sum) operators of bivariate -Bernstein type. For the first operators, we state the Volkov-type theorem and we obtain a Voronovskaja type and investigate the degree of approximation by means of the Lipschitz type space. For the GBS type operators, we establish their degree of approximation in terms of the mixed modulus of smoothness. The comparison of convergence of the bivariate -Bernstein type operators based on parameters and its GBS type operators is shown by illustrative graphics using MATLAB software.

中文翻译：

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相似双变量-Bernstein型算子的逼近性质

在这篇文章中，我们建立的二元泛化的延伸-含参Bernstein型算子和二元的GBS（广义布尔和）运营商的扩展-伯恩斯坦类型。对于第一个算子，我们陈述Volkov型定理，获得Voronovskaja型，并通过Lipschitz型空间研究近似度。对于GBS类型的算子，我们用混合的平滑模量确定它们的近似度。二元收敛的比较-基于参数和其GBS型算Bernstein型算子是通过使用MATLAB软件说明性图形所示。