properties of periodic function












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If $f$ is a continuous periodic function of period $2π$, then is there a point c such that $f(c+π/2)=f(c)$ and a point x such that $f(x+π/4)=f(x)$? domain of $f$ is $mathbb{R}$ and $f$ is real valued.










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  • $begingroup$
    $g(x)= f(x)-f(x+pi/2)$ is $2pi$-periodic and continuous. If it is strictly positive then so is $sum_{n=0}^3 g(x+npi/2) =...$
    $endgroup$
    – reuns
    Jan 20 at 6:39


















0












$begingroup$


If $f$ is a continuous periodic function of period $2π$, then is there a point c such that $f(c+π/2)=f(c)$ and a point x such that $f(x+π/4)=f(x)$? domain of $f$ is $mathbb{R}$ and $f$ is real valued.










share|cite|improve this question











$endgroup$












  • $begingroup$
    $g(x)= f(x)-f(x+pi/2)$ is $2pi$-periodic and continuous. If it is strictly positive then so is $sum_{n=0}^3 g(x+npi/2) =...$
    $endgroup$
    – reuns
    Jan 20 at 6:39
















0












0








0





$begingroup$


If $f$ is a continuous periodic function of period $2π$, then is there a point c such that $f(c+π/2)=f(c)$ and a point x such that $f(x+π/4)=f(x)$? domain of $f$ is $mathbb{R}$ and $f$ is real valued.










share|cite|improve this question











$endgroup$




If $f$ is a continuous periodic function of period $2π$, then is there a point c such that $f(c+π/2)=f(c)$ and a point x such that $f(x+π/4)=f(x)$? domain of $f$ is $mathbb{R}$ and $f$ is real valued.







real-analysis






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share|cite|improve this question













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share|cite|improve this question








edited Jan 20 at 5:51









Macrophage

1,191115




1,191115










asked Jan 20 at 5:31









jjjjjj

1094




1094












  • $begingroup$
    $g(x)= f(x)-f(x+pi/2)$ is $2pi$-periodic and continuous. If it is strictly positive then so is $sum_{n=0}^3 g(x+npi/2) =...$
    $endgroup$
    – reuns
    Jan 20 at 6:39




















  • $begingroup$
    $g(x)= f(x)-f(x+pi/2)$ is $2pi$-periodic and continuous. If it is strictly positive then so is $sum_{n=0}^3 g(x+npi/2) =...$
    $endgroup$
    – reuns
    Jan 20 at 6:39


















$begingroup$
$g(x)= f(x)-f(x+pi/2)$ is $2pi$-periodic and continuous. If it is strictly positive then so is $sum_{n=0}^3 g(x+npi/2) =...$
$endgroup$
– reuns
Jan 20 at 6:39






$begingroup$
$g(x)= f(x)-f(x+pi/2)$ is $2pi$-periodic and continuous. If it is strictly positive then so is $sum_{n=0}^3 g(x+npi/2) =...$
$endgroup$
– reuns
Jan 20 at 6:39












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