Approximation of fixed points for nonexpansive semigroups in Hilbert spaces

Fixexd point theory and applications

Yeong-Cheng Liou¹  Yeol Je Cho²  Yonghong Yao³  Jung Im Kang⁴ 

[1] Department of Information Management, Cheng Shiu University, Kaohsiung, Taiwan;Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju, Korea;Department of Mathematics, Tianjin Polytechnic University, Tianjin, China;National Institute for Mathematical Sciences, KT Daeduk 2 Research Center, Daejeon, Korea

关键词: nonexpansive semigroup;    common fixed point;    algorithms;    projection;   

DOI  :  10.1186/1687-1812-2013-31

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we propose two new algorithms for finding a common fixed point of a nonexpansive semigroup in Hilbert spaces and prove some strong convergence theorems for nonexpansive semigroups. Our results improve and generalize the corresponding results given by Shimizu and Takahashi (J. Math. Anal. Appl. 211:71-83, 1997), Shioji and Takahashi (Nonlinear Anal. TMA 34:87-99, 1998), Lau et al. (Nonlinear Anal. TMA 67:1211-1225, 2007) and many others. MSC:47H05, 47H10, 47H17.

【 授权许可】

CC BY