含若干参数泛函方程的解析表示及其Holder指数
发布时间：2019-05-21 10:02
【摘要】：在古典分析中讨论函数的连续性和可微性是一项重要内容,自从Weierstrass构造了连续不可微函数之后,越来越多的数学家开始致力于构造此类新的函数,并对其性质进行研究.借助含有参数r的广义三进制数系188工具,本文对广义Okamoto函数Fa,b,r(x)进行解析表示,并在此基础上研究其分形性质.基于3一自相似集的一种分类,对一类含参数泛函方程的解进行解析表示,并讨论其Holder指数等分形性质.
[Abstract]:It is an important content to discuss the continuity and differentiability of functions in classical analysis. Since Weierstrass constructed continuous nondifferentiable functions, more and more mathematicians have devoted themselves to constructing such new functions and studying their properties. With the help of the generalized ternary number system 188 tool with parameter r, this paper makes an analytical representation of the generalized Okamoto function Fa,b,r (x), and on this basis, studies its fractal properties. Based on a classification of three self-similar sets, the solutions of a class of functional equations with parameters are expressed analytically, and their fractal properties such as Holder index are discussed.
【学位授予单位】：云南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O189
本文编号：2482016
[Abstract]:It is an important content to discuss the continuity and differentiability of functions in classical analysis. Since Weierstrass constructed continuous nondifferentiable functions, more and more mathematicians have devoted themselves to constructing such new functions and studying their properties. With the help of the generalized ternary number system 188 tool with parameter r, this paper makes an analytical representation of the generalized Okamoto function Fa,b,r (x), and on this basis, studies its fractal properties. Based on a classification of three self-similar sets, the solutions of a class of functional equations with parameters are expressed analytically, and their fractal properties such as Holder index are discussed.
【学位授予单位】：云南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O189
【参考文献】
相关期刊论文 前6条
1 ;CONSTRUCTION OF SOME KIESSWETTER-LIKE FUNCTIONS-THE CONTINUOUS BUT NON-DIFFERENT-IABLE FUNCTION DEFINED BY QUINARY DECIMAL[J];Analysis in Theory and Applications;2004年01期
2 杨晓玲,陈丹;广义Sierpinski集[J];数学的实践与认识;2003年08期
3 杨晓玲;广义Cantor函数的解析表示[J];云南大学学报(自然科学版);2001年06期
4 张健,杨光俊;一类分形曲线的构造[J];云南大学学报(自然科学版);2002年03期
5 杨晓玲,黄雪梅;Koch曲线的级数展开式[J];应用数学学报;2002年03期
6 杨晓玲,杨光俊;Bush连续不可微函数的分形性质[J];应用数学学报;2005年03期
，本文编号：2482016
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