Strong convergence of an iterative algorithm for pseudocontractive mapping in Banach spaces

作者：Yao Yonghong^*; Liou Yeong Cheng; Chen Rudong

来源：Nonlinear Analysis-Theory Methods & Applications, 2007, 67(12): 3311-3317.

DOI：10.1016/j.na.2006.10.013

• strong convergence
• pseudocontractive mapping
• fixed point
• uniformly smooth Banach spaces

Let C be a nonempty closed convex subset of a real uniformly smooth Banach space X, T : C -> C a pseudocontractive mapping. Let {alpha(n)}, {beta(n)} and {gamma(n)} be three real sequences in (0, 1) satisfying appropriate conditions; then for fixed u epsilon C and arbitrary x(0) epsilon C, the sequence {x(n)} generated by
x(n) = alpha(n)u + beta(n)x(n)-1 + gamma(n)Tx(n), n >= 1, converges strongly to a fixed point of T.

• 出版日期2007-12-15
• 单位天津工业大学