Consider $1\le p,q < \infty , t\in \mathbb R , f,g>0$ then is $g(x)^q[f^pg^{-q} (x)]^t$ convex in the following context?
Thanks for help .
Consider $1\le p,q < \infty , t\in \mathbb R , f,g>0$ then is $g(x)^q[f^pg^{-q} (x)]^t$ convex in the following context?
Thanks for help .
Take $f^p(x)=g^q(x)=2+\cos x$, then $g^q[f^pg^{-q}]^t$ is not convex.