摘要
分形函数的研究在分形几何中占有重要的地位,在分形函数的研究中分形维数的讨论则是一个重要的数学手段。由迭代产生的分形函数的维数已基本解决。文中对另一类处处连续点点不可微函数进行了研究,并用网立方体与函数相交的方法对该分形函数的Box维数的上下界、填充维及Hausdorff维数上界进行了估计,同时讨论了该分形函数的Ho!lder条件,并把结果推广到了Bush函数,最终使该分形函数的一些分形性质得到了解决。
Analysis for a class of fractal functions plays a significant role in the fractal geometry, and the discussion about fractal dimensions is an important mathematical method in the study of fractal dimensions. Dimensions of fractal functions produced by iterated function systems have been solved. A class of functions which are everywhere continuous and nowhere differentiable are analyzed. Using the intersection of mesh squares and functions, some estimate respectively for upper and lower bound of Box , Packing and upper bound of Hausdorff dimensions is given ,besides the fractal functions＂ Holder condition is discussed, and the result to Bush function is extended, so some important characters of the fractal function are got at last.
出处
《安徽工业大学学报（自然科学版）》
CAS
2006年第3期356-359,共4页
Journal of Anhui University of Technology（Natural Science）
基金
国家自然科学基金资助项目(10571076)
