Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
844466 | Nonlinear Analysis: Theory, Methods & Applications | 2007 | 9 Pages |
Abstract
Let E be a real strictly convex Banach space with a uniformly Gâteaux differentiable norm, and K be a nonempty closed convex subset of E. Suppose that {Tn}(n=1,2,â¦) is a uniformly asymptotically regular sequence of nonexpansive mappings from K to itself such that Fâân=1âF(Tn)â 0̸. For arbitrary initial value x0âK and fixed contractive mapping f:KâK, define iteratively a sequence {xn} as follows: xn+1=λn+1f(xn)+(1âλn+1)Tn+1xn,nâ¥0, where {λn}â(0,1) satisfies limnââλn=0 and ân=1âλn=â. Suppose for any nonexpansive mapping T:KâK, {zt} strongly converges to a fixed point z of T as tâ0, where {zt} is the unique element of K which satisfies zt=tf(zt)+(1ât)Tzt. Then as nââ, xnâz. Our results extend and improve the corresponding ones of O'Hara et al. [J.G. O'Hara, P. Pillay, H.-K. Xu, Iterative approaches to finding nearest common fixed point of nonexpansive mappings in Hilbert spaces, Nonlinear Anal. 54 (2003) 1417-1426] and J.S. Jung [Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 302 (2005) 509-520] and H.K. Xu [Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. 298 (2004) 279-291].
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Authors
Yisheng Song, Rudong Chen, Haiyun Zhou,