In this paper, we introduce a new family of generalized blending-type bivariate Bernstein operators which depends on four parameters \(s_{1}\), \(s_{2}\), \(\alpha _{1}\) and \(\alpha _{2}\). Approximation properties of these operators are studied, and we obtain the rate of convergence in terms of mixed and partial modulus of continuities. Moreover, we prove a Korovkin- and a Voronovskaja-type theorems for these operators. The last part of the paper is devoted to the associated GBS operators. In this part, we study degree of approximation of the GBS operators in terms of mixed modulus of continuity. GBS operators obtained here give better approximation than the original operators to the function f(x, y). Finally, approximation properties of the suggested operators and their associated GBS operators are discussed on graphs, for some numerical examples to show how GBS operator gives better approximation to f(x, y). Also, approximation properties of the suggested operators for different values of parameters \(s_{1}\), \(s_{2}\), \(\alpha _{1}\) and \(\alpha _{2}\) are illustrated on graphs. It should be mentioned that any increase in \(\alpha _{i}\) values or any decrease in \(s_{i}\) values gives better approximation of the suggested operators to f(x, y).

在本文中，我们介绍了一个新的广义混合类型双变量Bernstein算子族，该算子依赖于四个参数\（s_ {1} \），\（s_ {2} \），\（\ alpha _ {1} \）和\（\ alpha _ {2} \）。研究了这些算子的逼近性质，我们得到了混合的连续性和部分连续模量的收敛速度。此外，我们证明了这些算子的Korovkin型和Voronovskaja型定理。本文的最后一部分专门介绍了相关的GBS运营商。在这一部分中，我们将根据混合连续模量研究GBS算子的近似程度。在此获得的GBS运算符对函数f（x，  y）。最后，在图形上讨论了建议算子及其相关GBS算子的逼近性质，并通过一些数值示例来说明GBS算子如何更好地逼近f（x，  y）。此外，建议的算子对参数\（s_ {1} \），\（s_ {2} \），\（\ alpha _ {1} \）和\（\ alpha _ {2}的不同值的近似性质\）在图表上显示。应该指出的是，\（\ alpha _ {i} \）值的任何增加或\（s_ {i} \）值的任何减少都可以将建议的运算符更好地近似为f（x，  y）。