Assume that a strictly increasing function g: R →R exists such that g(0)=0, and a norm g(f(x))

Question

Assume that a strictly increasing function g: R →R exists such that g(0)=0, and a norm g(f(x))<g

Accepted Answer

Step 1: Understand the problem context. We have a strictly increasing function u005C( g: u005Cmathbb{R}

Assume that a strictly increasing function $g: R \rightarrow R$ exists such that $g(0)=0$, and a norm $g(\|f(x)\|)<g(b x \|)$ for all $x \neq 0$. Then show that 0 is globally symptotically stable equilibrium for equation $x(t+1)=f(x(t))$, where $f(0)=0$.