Fejér monotonicity
= Fejér monotonicity
{c}
{title2=$\|z^{k+1}-p\|\leq\|z^k-p\|$}
A sequence is Fejér monotone with respect to a nonempty set $C$ if $\|z^{k+1}-p\|\leq\|z^k-p\|$ for every $p\in C$. It is bounded. If it has a cluster point $\bar z\in C$, its nonincreasing distance to $\bar z$ and that convergent subsequence force the entire sequence to converge to $\bar z$.