$f$ is the output of a discrete time process described by
$f(k)=\sum\limits_{i=1}^{k-1}w_{ki}f(i)$
where $f(1)\geq0$ is a known initial condition and $w_{ki}\geq0$ are weights of previous states on the future states. Is it possible to derive a condition on the weights $w_{ki}$ such that the output is non-decreasing, i.e. $f(1)\leq f(2)\leq\cdots\leq f(k)\leq f(k+1)$
I feel expressing all subsequent states $f(k)$ directly in terms of $f(1)$ might help, but somehow the expression becomes unmanageable.