I try to find the example to show this
If $f_{n}\overset{w*}{\rightarrow} f$ and $x_{n}\overset{w}{\rightarrow}x$ not necessarily $f_{n}(x_{n}) \rightarrow f(x)$.
prove the $f_{n}(x_{n})\rightarrow f(x)$ in the case $x_{n}\overset{||.||}{\rightarrow}x$ is so easy but find the example for the another case is hard for me.