WEAK AND STRONG CONVERGENCE OF AN ITERATIVE METHOD FOR NONEXPANSIVE MAPPINGS IN HILBERT SPACES

In a real {sc Hilbert} space $H$, starting from an arbitrary initialpoint $x_0in H$, an iterative process is defined as follows:$x_{n+1}=a_nx_n+(1-a_n)T^{lambda_{n+1}}_fy_n$, $y_n= b_nx_n+(1-b_n)T^{eta_{n}}_gx_n$, $nge 0$, where$T^{lambda_{n+1}}_f x= Tx-lambda_{n+1} mu_f f(Tx)$,$T^{eta_{n}}_g x= Tx-eta_{n} mu_g g(Tx)$, ($forall xinH$), $T: H o H$ a nonexpansive mappingwith $F(T) eemptyset$ and $f$ (resp. $g$) $: H o H$ an$eta_f$ (resp. $eta_g$)-strongly monotone and $k_f$ (resp. $k_g$)-Lipschitzianmapping, ${a_n}subset(0,1)$, ${b_n}subset(0,1)$ and ${lambda_n}subset[0,1)$,${eta_n}subset[0,1)$. Under some suitable conditions, severalconvergence results of the sequence ${x_n}$ are shown.