Modified mann iterations for nonexpansive semigroups in Banach space

Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E*, and C be a nonempty closed convex subset of E. Let {T(t): t ≥ 0} be a nonexpansive semigroup on C such that F:= ∩ _t≥0 Fix(T(t)) ≠ ∅, and f: C → C be a fixed contractive mapping. If {α _n }, {β _n }, {a _n }, {b _n }, {t _n } satisfy certain appropriate conditions, then we suggest and analyze the two modified iterative processes as:

$ \left\{ {{*{20}c} {y_n = \alpha _n x_n + (1 - \alpha _n )T(t_n )x_n ,} \\ {x_n = \beta _n f(x_n ) + (1 - \beta _n )y_n .} \\ } \right. $ \left\{ {\begin{array}{*{20}c} {y_n = \alpha _n x_n + (1 - \alpha _n )T(t_n )x_n ,} \\ {x_n = \beta _n f(x_n ) + (1 - \beta _n )y_n .} \\ \end{array} } \right.
Keywords:	fixed point  nonexpansive semigroups  strong convergence  reflexive Banach space
本文献已被 维普 SpringerLink 等数据库收录！