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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 $$\underset{u,\eta \in V}{sup}\left\{r(u,\eta )\right\}=\lambda <\infty$$ $${r(u,\eta )\parallel J(u-\eta )\parallel }_{V^{☆}}\ge {\parallel (J-F)\left(u\right)-(J-F)\left(\eta \right)\parallel }_{V^{☆}},\forall u,\eta \in V.$$ Furthermore, the case when $V$ is a Hilbert space is given. An application of our results to...