论文标题
多元拉链分形功能
Multivariate Zipper Fractal Functions
论文作者
论文摘要
提出了一种针对多个变量功能的拉链分形插值理论的新方法。我们以建设性的方式开发多元拉链分形功能。然后，我们通过自由选择基本函数，缩放函数和称为签名的二进制矩阵来驱动多元函数，以构建其拉链$α$ farctal品种。特别是，我们提出了多元伯恩斯坦拉链分形功能，并研究其近似特性，例如保留形状的方面，非负和坐标的单调性。此外，我们通过对缩放因子和相关的细菌函数和基本功能的缩放因子和Hölder指数施加条件来得出多元拉链分形函数图的边界。还研究了多元伯恩斯坦功能的LIPSCHITZ连续性，以获取多变量Bernstein拉链分形功能的盒子尺寸的估计。
A novel approach to zipper fractal interpolation theory for functions of several variables is proposed. We develop multivariate zipper fractal functions in a constructive manner. We then perturb a multivariate function to construct its zipper $α$-fractal varieties through free choices of base functions, scaling functions, and a binary matrix called signature. In particular, we propose a multivariate Bernstein zipper fractal function and study its approximation properties such as shape preserving aspects, non-negativity, and coordinate-wise monotonicity. In addition, we derive bounds for the graph of multivariate zipper fractal functions by imposing conditions on the scaling factors and the Hölder exponent of the associated germ function and base function. The Lipschitz continuity of multivariate Bernstein functions is also studied in order to obtain estimates for the box dimension of multivariate Bernstein zipper fractal functions.
