On the Hölder continuity of certain functions
The authors prove a theorem giving some sufficient conditions under which a real function of the form \(f(x)=\sum^{\infty}_{n=0}f_ n(x)\) is Hölder continuous. The Hölder continuity of the van der Waerden's function \(f(x)=\sum^{\infty}_{n=0}2^{-n}d(2^ nx,{\mathbb{Z}})\) and of the Weierstrass' functions \(f(x)=\sum^{\infty}_{n=0}a^ n \cos b^ n\pi x,\quad 0<a<1,\quad ab\geq 1,\) is obtained as a corollary of the theorem.
scientific article; zbMATH DE number 4198359