In this paper, we construct a new kind of weighted recursive iteration function system (IFS) and prove the existence of the unique attractor for the kind of IFS based on the Matkowski fixed point theorem. We confirm that the attractor is a bivariate fractal interpolation surface (FIS), which interpolates a given set of data. In addition, we also provide an upper error estimate of such FISs caused by changes of weights. Finally, we give their box dimension estimates for a specific type of the FISs.

中文翻译：

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基于Matkowski收缩的加权分形插值面构造

本文构造了一类新型的加权递归迭代函数系统(IFS)，并基于Matkowski不动点定理证明了该类IFS唯一吸引子的存在性。我们确认吸引子是一个二元分形插值曲面（FIS），它对给定的数据集进行插值。此外，我们还提供了由权重变化引起的此类 FIS 的上限误差估计。最后，我们给出了特定类型 FIS 的盒子尺寸估计。