WEAK AND STRONG CONVERGENCE OF AN ITERATIVE METHOD FOR NONEXPANSIVE MAPPINGS IN HILBERT SPACES
Titel:
WEAK AND STRONG CONVERGENCE OF AN ITERATIVE METHOD FOR NONEXPANSIVE MAPPINGS IN HILBERT SPACES
Auteur:
Junfen Li Yu Miao
Verschenen in:
Applicable analysis and discrete mathematics
Paginering:
Jaargang 2 (2008) nr. 2 pagina's 197-204
Jaar:
2008
Inhoud:
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$T^{lambda_{n+1}}_f x= Tx-lambda_{n+1} mu_f f(Tx)$,$T^{eta_{n}}_g x= Tx-eta_{n} mu_g g(Tx)$, ($forall xinH$), $T: Ho H$ a nonexpansive mappingwith $F(T) eemptyset$ and $f$ (resp. $g$) $: Ho H$ 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.
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