【摘要】：在古典分析中討論函數(shù)的連續(xù)性和可微性是一項(xiàng)重要內(nèi)容,自從Weierstrass構(gòu)造了連續(xù)不可微函數(shù)之后,越來(lái)越多的數(shù)學(xué)家開始致力于構(gòu)造此類新的函數(shù),并對(duì)其性質(zhì)進(jìn)行研究.借助含有參數(shù)r的廣義三進(jìn)制數(shù)系188工具,本文對(duì)廣義Okamoto函數(shù)Fa,b,r(x)進(jìn)行解析表示,并在此基礎(chǔ)上研究其分形性質(zhì).基于3一自相似集的一種分類,對(duì)一類含參數(shù)泛函方程的解進(jìn)行解析表示,并討論其Holder指數(shù)等分形性質(zhì).
[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.
【學(xué)位授予單位】：云南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O189

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本文編號(hào)：2482016