strong convergence theorems of the general iterative methods for nonexpansive semigroups in banach spaces
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2011
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Abstract
Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E*. Let S={T(s):0≤s<∞} be a nonexpansive semigroup on E such that Fix(S):=⋂t≥0Fix(T(t))≠∅, and f is a contraction on E with coefficient 0<α<1. Let F be δ-strongly accretive and λ-strictly pseudocontractive with δ+λ>1 and γ a positive real number such that γ<1/α(1-1-δ/λ). When the sequences of real numbers {αn} and {tn} satisfy some appropriate conditions, the three iterative processes given as follows: xn+1=αnγf(xn)+(I-αnF)T(tn)xn, n≥0, yn+1=αnγf(T(tn)yn)+(I-αnF)T(tn)yn, n≥0, and zn+1=T(tn)(αnγf(zn)+(I-αnF)zn), n≥0 converge strongly to x̃, where x̃ is the unique solution in Fix(S) of the variational inequality 〈(F-γf)x̃,j(x-x̃)〉≥0, x∈Fix(S). Our results extend and improve corresponding ones of Li et al. (2009) Chen and He (2007), and many others.
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| Reference Key |
wangkeeree2011internationalstrong
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|---|---|
| Authors | ;Rattanaporn Wangkeeree |
| Journal | structural engineering and mechanics |
| Year | 2011 |
| DOI |
10.1155/2011/643740
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| URL | |
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