Strong convergence theorems for finitely many nonexpansive mappings

作者：Song Yisheng^*; Zuo Hongliang

来源：Nonlinear Analysis-Theory Methods & Applications, 2009, 70(4): 1797-1802.

DOI：10.1016/j.na.2008.02.078

• Non-expansive mappings
• Weakly continuous duality mapping

Under the assumption that E is a reflexive Banach space whose norm is uniformly Geteaux differentiable and which has a weakly continuous duality mapping J(phi) with gauge function phi, Ceng-Cubiotti-Yao [Strong convergence theorems for finitely many, nonexpansive mappings and applications, Nonlinear Analysis 67 (2007) 1464-1473] introduced a new iterative scheme for,I finite commuting family of nonexpansive mappings, and proved strong convergence theorems about this iteration. In this paper, only under the hypothesis that E is a reflexive Banach space which has a weakly continuous duality mapping J(phi) with gauge function phi, and several control conditions about the iterative coefficient arc removed, we present a short and simple proof of the above theorem.

• 出版日期2009-2-15
• 单位河南师范大学