A property of C1,α functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:435

Article

关键词: C-1,C-alpha functions;    Differentiability;   

DOI  :  10.1016/j.jmaa.2015.10.051

来源: Elsevier

【 摘 要 】

In this note we show that, if f >= 0 is a differentiable function on [0,T] having a Holder continuous derivative with exponent a in (0,1], and if f'(0) = 0 (resp. f'(T) = 0) when f(0) = 0 (resp. f (T) 0), then for all mu is an element of (1/(1 + alpha),1) f(mu) is an element of C-1[0, T]. Moreover (f(mu))' is Holder continuous with exponent beta = mu(1 + alpha) - 1 (resp. alpha) at x is an element of [0, T] when f(x)= 0 (resp. f(x) > 0). (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free