dagrgGS
Oct6-10, 07:26 AM
Let a,b,x,y\in\mathbb{R} and f\left(a,b\right)=
\max_{\left|x\right|,\left|y\right|,\left|ax+by\ri ght|\leq1}\left(\left|x+y\right|,\left|x-y\right|,\left|\left(a+1\right)x+\left(b-2\right)y\right|\right)
Then what is the infimum of f\left(a,b\right) for \left(a,b\right)\in\mathbb{R}^2?
Thanks for any helpful answers.
\max_{\left|x\right|,\left|y\right|,\left|ax+by\ri ght|\leq1}\left(\left|x+y\right|,\left|x-y\right|,\left|\left(a+1\right)x+\left(b-2\right)y\right|\right)
Then what is the infimum of f\left(a,b\right) for \left(a,b\right)\in\mathbb{R}^2?
Thanks for any helpful answers.