Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 484050, 13 pages
doi:10.1155/2008/484050
Composite implicit general iterative process for a nonexpansive semigroup in Hilbert space
Lihua Li1
, Suhong Li1
and Yongfu Su3
1Department of Mathematic and Physics, Hebei Normal University of Science and Technology Qinhuangdao, Hebei 066004, China
3Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
Abstract
Let C be nonempty closed convex subset of real Hilbert space H. Consider C a nonexpansive semigroup ℑ={T(s):s≥0} with a common fixed point, a contraction f with coefficient 0<α<1, and a strongly positive linear bounded operator A with coefficient γ¯>0. Let 0<γ<γ¯/α. It is proved that the sequence {xn} generated iteratively by xn=(I−αnA)(1/tn)∫0tnT(s)ynds+αnγf(xn),yn=(I−βnA)xn+βnγf(xn) converges strongly to a common fixed point x∗∈F(ℑ) which solves the variational inequality 〈(γf−A)x∗,z−x∗〉≤0 for all z∈F(ℑ).