کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4618096 1339398 2011 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An inequality for sums of binary digits, with application to Takagi functions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
An inequality for sums of binary digits, with application to Takagi functions
چکیده انگلیسی

Let ϕ(x)=2inf{|x−n|:n∈Z}ϕ(x)=2inf{|x−n|:n∈Z}, and define for α>0α>0 the functionfα(x)=∑j=0∞12αjϕ(2jx). Tabor and Tabor [J. Tabor, J. Tabor, Takagi functions and approximate midconvexity, J. Math. Anal. Appl. 356 (2) (2009) 729–737] recently proved the inequalityfα(x+y2)⩽fα(x)+fα(y)2+|x−y|α, for α∈[1,2]α∈[1,2]. By developing an explicit expression for fαfα at dyadic rational points, it is shown in this paper that the above inequality can be reduced to a simple inequality for weighted sums of binary digits. That inequality, which seems of independent interest, is used to give an alternative proof of the result of Tabor and Tabor, which captures the essential structure of fαfα.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 381, Issue 2, 15 September 2011, Pages 689–694
نویسندگان
,