$7.$ Define the sequence $\{$un$\}$ by

u$0($t$)=$ x$0,$

un$+1=$ x$0+$

$$ t

t$0$

f$($s$,$ un$($s$))$ ds$,$ n $=1,2,....$

Use the result of the previous exercise to show that

$|$f$($t$,$ un$($t$))$ f$($t$,$ un$1($t$))|<=$ K$|$un$($t$)$ un$1($t$)|$