. Let $a:(-\infty,0]\rightarrow[0,1]$, be a monotone non decreasing function such that for some $B>0$, $\delta>0$ the inequality

$$t\,a(s)\leq B\,a(s+t)^{1+\delta}$$

holds for all $s\leq 0,\,t\in[0,1],\,s+t\leq 0$. Then for all $S<0$ such that $a(S)>0$ and all $D\in[0,1],\,S+D\leq 0$ we have the estimate

$$D\leq e(3+2/\delta)B\,a(S+D)^{\delta}\,.$$