کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8899581 1631548 2018 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Doubly paradoxical functions of one variable
ترجمه فارسی عنوان
عملکرد دوگانه متناقض یک متغیر
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی
This paper concerns three kinds of seemingly paradoxical real valued functions of one variable. The first two, defined on R, are the celebrated continuous nowhere differentiable functions, known as Weierstrass's monsters, and everywhere differentiable nowhere monotone functions-simultaneously smooth and very rugged-to which we will refer as differentiable monsters. The third kind was discovered only recently and consists of differentiable functions f defined on a compact perfect subset X of R which has derivative equal zero on its entire domain, making it everywhere pointwise contractive, while, counterintuitively, f maps Xonto itself. The goal of this note is to show that this pointwise shrinking globally stable map f can be extended to functions f,g:R→R which are differentiable and Weierstrass's monsters, respectively. Thus, we pack three paradoxical examples into two functions. The construction of f is based on the following variant of Jarník's Extension Theorem: For every differentiable function f from a closedP⊆RintoRthere exists its differentiable extensionfˆ:R→Rsuch thatfˆis nowhere monotone onR∖P.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 464, Issue 1, 1 August 2018, Pages 274-279
نویسندگان
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