In this paper, we study shape preserving aspects of bivariate α-fractal functions. Its specific aims are: (i) to solve the range restricted problem for bivariate fractal approximation (ii) to establish the fractal analogue of lionized Weierstrass theorem of bivariate functions (iii) to study the constrained approximation by 𝒞r-bivariate α-fractal functions (v) to investigate the conditions on the parameters of the iterated function system in order that the bivariate α-fractal function fα preserves fundamental shapes, namely, positivity and convexity (concavity) in addition to the smoothness of f over a rectangle (vi) to establish fractal versions of some elementary theorems in the shape preserving approximation of bivariate functions.

中文翻译：

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双变量α-分形函数的形状保持方面

在本文中，我们研究了双变量的形状保持方面α-分形函数。其具体目标是：(i) 解决二元分形逼近的范围受限问题 (ii) 建立二元函数的 Lionized Weierstrass 定理的分形类比 (iii) 研究约束逼近𝒞r-双变量α-分形函数 (v) 研究迭代函数系统的参数条件，以使双变量α-分形函数Fα除了平滑度之外，还保留了基本形状，即正性和凸度（凹度）F在矩形 (vi) 上建立一些基本定理的分形版本，以保持双变量函数的形状近似。