The weak convergence of the iterative generated by $J(u_{n+1}-u_n)=\tau (F{u}_n-J{u}_n)$, $n\ge 0$, $(0<\tau =min\{1,\frac{1}{\lambda }\})$ to a coincidence point of the mappings $F,J:V\to V^{☆}$ is investigated, where $V$ is a real reflexive Banach space and $V^{☆}$ its dual (assuming that $V^{☆}$ is strictly convex). The basic assumptions are that $J$ is the duality mapping, $J-F$ is demiclosed at $0$, coercive, potential and bounded and that there exists a non-negative real valued function $r(u,\eta )$ such that $$\underset{u,\eta \in V}{sup}\left\{r(u,\eta )\right\}=\lambda <\infty$$$$...$$

Ram’ırez-Páramo proved that under GCH for the class of compact Hausdorff spaces i-weight reflects all cardinals [A reflection theorem for i-weight, Topology Proc. 28 (2004), no. 1, 277–281]. We show that in ZFC i-weight reflects all cardinals for the class of compact LOTS. We define local i-weight, then calculate i-weight of locally compact LOTS and paracompact spaces in terms of the extent of the space and the i-weight of open sets or the local i-weight. For locally compact LOTS we find a necessary...