Convergence analysis of iterative sequences for a pair of mappings in Banach spaces

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• 作者：Liu Chuan Zeng ; N. C. Wong and J. C. Yao
• 关键词：quasi ; nonexpansive mapping ; asymptotically demicontractive type mapping ; iterative sequence ; convergence analysis
• 刊名：Acta Mathematica Sinica
• 出版年：2008
• 出版时间：March, 2008
• 年：2008
• 卷：24
• 期：3
• 页码：463-470
• 全文大小：167.0 KB

文摘

Let C be a nonempty closed convex subset of a real Banach space E. Let S: C → C be a quasi-nonexpansive mapping, let T: C → C be an asymptotically demicontractive and uniformly Lipschitzian mapping, and let F:= {x ε C: Sx = x and Tx = x} ≠ 0. Let {x _n } _n≥0 be the sequence generated from an arbitrary x ₀ ε C by $ x_{n + 1} = (1 - c_n )Sx_n + c_n T^n x_n , n \geqslant 0. $ x_{n + 1} = (1 - c_n )Sx_n + c_n T^n x_n , n \geqslant 0.