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STRONG CONVERGENCE OF APPROXIMATED SEQUENCES FOR NONEXPANSIVE MAPPINGS IN BANACH SPACES 被引量:2

STRONG CONVERGENCE OF APPROXIMATED SEQUENCES FOR NONEXPANSIVE MAPPINGS IN BANACH SPACES
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摘要 This paper studies the convergence of the sequence defined by x0 ∈ C, xn+l =αnu+(1-αn)Txn, n=0, 1,2,..., where 0 ≤αn ≤ 1, limn→∞ αn = 0, ∑n=0^∞ αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results. This paper studies the convergence of the sequence defined by x0 ∈ C, xn+l =αnu+(1-αn)Txn, n=0, 1,2,..., where 0 ≤αn ≤ 1, limn→∞ αn = 0, ∑n=0^∞ αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results.
机构地区 Dept. of Math.
出处 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2007年第3期311-315,共5页 高校应用数学学报(英文版)(B辑)
基金 Supported by the Natural Science Foundation of the Educational Dept.of Zhejiang Province(20020868).
关键词 nonexpansive mapping uniformly convex Banach space uniformly smooth Banach space Banach limit. nonexpansive mapping, uniformly convex Banach space, uniformly smooth Banach space, Banach limit.
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  • 1Halpern B.Fixed points of nonexpansivemaps,Bull Amer Math Soc,1967,73:957-961.
  • 2Lions P L.Approximation de points fixes de contractions,C R Acad pari SerA,1977,284:1357-1359.
  • 3Reich S.Strong convergence theorems for resolvents of accretive operators in Banachspaces,J Math Anal Appl,1980,75:287-292.
  • 4Wittmann R.Approximation of fixed points of nonexpansive mappings,ArchMath,1992,58:486-491.
  • 5Reich S.Approximating fixed points of nonexpansive mappings,Pan Amer MathJ,1994,4(2):23-28.
  • 6Shioji N,Takahashi W.Strong convergence of approximated sequences for nonexpansivemappings in Banach spaces,Proc Amer Math Soc,1997,125(12):3641-3645.
  • 7Shimizu T,Takahashi W.Strong convergence to common fixed points of families ofnonexpansive mappings in Banach spaces,J Math Anal Appl,1997,211(1):71-83.
  • 8Zhang S S,Tian Y X.On the Halpern's open question,Acta MathematicaSinica,2005,48:979-984.
  • 9Aksoy A G,Khamsi M A.Nonstandard methods in fixed point theory,NewYork/Berlin:Springer-verlag,1990.
  • 10Bynum W L.Normal structure coefficient for Banach spaces,Pacific JMath,1980,86:427-436.

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