pow:problem3s25
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| pow:problem3s25 [2025/03/15 16:43] – created mazur | pow:problem3s25 [2025/03/24 05:43] (current) – mazur | ||
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| + | <box 85% round orange| Problem 3 (due Monday, March 17 )> | ||
| + | Let $f:\mathbb R\longrightarrow \mathbb R$ be an even continuous function such that $f(x+2)=f(x)$ for all $x$ | ||
| + | and $f$ is increasing on $[0,1]$. Define a new function $g:\mathbb R\longrightarrow \mathbb R$ by | ||
| + | \[ g(x)=\int_{0}^{2}f(t)f(t+x)\text{d}t.\] | ||
| + | Prove that $g(1)$ is the smallest value of $g$. | ||
| + | </ | ||
| + | |||
| + | The problem was solved by Ashton Keith (Purdue University), | ||
| + | For details see the following link {{: | ||