I was solving this problem $$ \|x\|\le \max\{ \|x-y\|,\|x+y\| \} $$ In $\mathbb{R}^n$ it looks trivial but how will I proceed in arbitrary normed linear space. Give me some hint to proceed. Although I have tried many inequalities but unable to get it. So please give me some hint so that I can do this.
Thanks!
Hint: $2||x|| = ||2x|| = ||(x + y) + (x - y)|| \leq ||x + y|| + ||x - y||$.