A hybrid iterative scheme for asymptotically k-strict pseudo-contractions in Hilbert spaces

作者：Qin Xiaolong; Cho Yeol Je^*; Kang Shin Min; Shang Meijuan

来源：Nonlinear Analysis-Theory Methods & Applications, 2009, 70(5): 1902-1911.

DOI：10.1016/j.na.2008.02.090

• Nonexpansive mapping
• Strict pseudo-contraction
• Asymptotically k-strict pseudo-contraction
• Fixed point

In this paper, we introduce an explicit iterative process for a finite family of asymptotically k-strict pseudo-contractions. By using the iterative process, we get a weak convergence theorem for a finite family of asymptotically k-strict pseudo-contractions and then we modify these algorithms to have strong convergence in the framework of Hilbert spaces. Our results improve and extend the recent ones announced by [G.L. Acedo, H.K. Xu, Iterative methods for strict pseudo-contractions in Hilbert spaces, Nonlinear Anal. 67 (2007) 2258-2271; T.H. Kim, H.K. Xu, Strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140-1152; C. Martinez-Yanes, H.K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411; K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379; G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert space, J. Math. Anal. Appl. 329 (2007) 336-346; TH. Kim, H.K. Xu, Convergence of the modified Manns iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal. (2007), doi:10.1016/j.na.2007.02.029] and many others.

• 出版日期2009-3-1
• 单位石家庄学院