How can I solve this problem?
Let $$x(n+1)=-\frac{\exp(x(n)/2)}{5}$$ be a given sequence. Prove using the Banach contraction principle that this sequence converges to some fixed point $X$ with $x(0)$ in some interval $[a,0]$ where $a<-1/5$.
How can I solve this problem?
Let $$x(n+1)=-\frac{\exp(x(n)/2)}{5}$$ be a given sequence. Prove using the Banach contraction principle that this sequence converges to some fixed point $X$ with $x(0)$ in some interval $[a,0]$ where $a<-1/5$.