Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Define functions $f_n\colon [0,1]\to\Bbb R$ by $f_n(x)=n^px\exp(-n^qx)$ where $p$, $q>0$ and $f_n\to 0$ pointwise on $[0,1]$ as $n\to \infty$ and $\sup|f_n(x)|=(n^{p-q})/e$.

Assume that $\epsilon\in (0,1)$; does $\{f_n\}$ converges uniformly on $[1-\varepsilon,1]$? How about on $[0,1-\varepsilon]$?

My idea is checking whether $f_n$ is continuous on the interval above, but it seems difficult. Can someone give me any idea?

share|improve this question

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.