Fixed-point solutions of variational inequalities for nonexpansive semigroups in Hilbert spaces
- 作者：Somyot Plubtieng ; Rattanaporn Punpaeng
- 关键词：Fixed point ; Variational inequality ; Viscosity approximation ; Nonexpansive semigroup ; Strong convergence
- 刊名：Mathematical and Computer Modelling
- 出版年：2008
- 期刊代码：86_08957177
- 类别：cp
- 出版时间：July 2008
- 卷：48
- 期：1-2
- 页码：279-286
- 文件大小：236 K
摘要
Let C be a nonempty closed convex subset of real Hilbert space H and 
be a nonexpansive semigroup on C such that 
. For a contraction f on C, and t
(0,1), let xtC be the unique fixed point of the contraction 
, where {λt} is a positive real divergent net. Consider also the iteration process {xn}, where x0C is arbitrary and 
for n≥0, where {
n},{βn}
(0,1) with n+βn<1 and 1a55bad0977ffea38fb4555270" title="Click to view the MathML source" alt="Click to view the MathML source">{sn} are positive real divergent sequences. It is proved that {xt} and, under certain appropriate conditions on {n} and {βn}, {xn} converges strongly to a common fixed point of 
.
(0,1), let xtC be the unique fixed point of the contraction C is arbitrary and n},{βn}(0,1) with n+βn<1 and 1a55bad0977ffea38fb4555270" title="Click to view the MathML source" alt="Click to view the MathML source">{sn} are positive real divergent sequences. It is proved that {xt} and, under certain appropriate conditions on {n} and {βn}, {xn} converges strongly to a common fixed point of