Banach空间中渐近非扩张映射逼近序列的强收敛性

Abstract

Abstract:

In this paper, the author studies the convergence of the sequence defined by x_0∈C,x_{n+1}=α_n T^n x_n+(1-α_n)x, n=0,1,2,…,where 0≤α_n≤1and T is an asymptotically nonexpansive mapping from a closed convex subset of a Banach space into itself and it is proved that, if lim_{n→∞}{(k_n-1)/(1-t_n)}=0,lim‖z_n-Tz_n‖=0 holds, then T has a fixed point if and only if {z_n} remains bounded as n→∞, in this case {z_n} converges strongly to a fixed point of T

Key words: Asymptotically nonexpansive mapping, Strong convergence, Banach limits

CLC Number:

47H09

HU Chang-Song. Strong Convergence of Approximated Sequences for Asymptotically Nonexpansive Mappings in Banach Spaces[J].Acta mathematica scientia,Series A, 2004, 24(2): 216-222.

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Strong Convergence of Approximated Sequences for Asymptotically Nonexpansive Mappings in Banach Spaces

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