We provide a general framework to construct fractal interpolation surfaces (FISs) for a prescribed countably infinite data set on a rectangular grid. Using this as a crucial tool, we obtain a parameterized family of bivariate fractal functions simultaneously interpolating and approximating a prescribed bivariate continuous function. Some elementary properties of the associated nonlinear (not necessarily linear) fractal operator are established, thereby initiating the interaction of the notion of fractal interpolation with the theory of nonlinear operators.

翻译：我们提供了一个用于构建矩形网格上可计算无限数据集的分形内插表面(FISs)的总框架。我们利用这个关键工具,获得了一个双轨分形函数的参数化组合,同时将一个指定的双轨连续函数相互插入和相近。建立了相关非线性(不一定是线性)分形操作员的一些基本特性,从而开始了分形内插概念与非线性操作员理论的相互作用。