关于渐近非扩张映象不动点的一个注记

程从沈,程丛电

(1.沈阳大学 理学院,辽宁 沈阳 110041;2.沈阳师范大学 数学与系统科学学院,辽宁 沈阳 110034)

关于渐近非扩张映象不动点的一个注记

程从沈1,程丛电2

(1.沈阳大学 理学院,辽宁 沈阳 110041;2.沈阳师范大学 数学与系统科学学院,辽宁 沈阳 110034)

设E是具一致 Gǎteaux可微范数的实Banach空间,D是E的一个凸子集·对于序列{kn}⊂[0,∞)的渐近非扩张映象T,赵良才和张石生在一定条件下给出并证明了关于T的具误差的Ishikawa迭代序列收敛于T的不动点·证明了这一结论对于一般的渐近非扩张映象也是成立的·

渐近非扩张映象;Ishikawa迭代序列;收敛;不动点

[1] GoebelK,Kirk W A. A fixedpointtheorem for asymptotically nonexpansive mappings[J].Proc.Amer.Math.Soc.,1972,35(1):171-174.

[2] Chang S S.On Chidume’s open questions and approximation solutions of multivalued strongly accretive mappings equations in Banach spaces[J].J.Math.Anal.Appl.,1997,216:94-111.

[3] Liu L S.Ishikawa and Mann iterative processes with errorsfor nonlinear strongly accretive mappings in Banach spaces[J].J.Math.Anal.Appl.,1995,194:114-125.

[4] 赵良才,张石生·Banach空间中渐进非扩张型映象具误差的强收敛定理[J]·数学学报,2008,51(1):99-108·

[5] Chidume C E,Li J,Udomene A.Convergence of paths and approximation of fixed points of asymptotically nonexpansive mappings[J].Proc.Amer.Math.Soc.,2004,133(2):473-480.

[6] Chang S S,Lee H W J,Chan C K.On Reich’s strong convergence theorem for asymptotically nonexpansive mappings in Banach spaces[J].Nonlinear Anal.TMA,2007,66:2364-2374.

A Note on Fixed Point of Asymptotically Nonexpansive Mapping

CHEN G Congshen1,CN EN G Congdian2

(1.School of Science,Shenyang University,Shenyang 110041,China;2.College of Mathematics and Systems Science,Shenyang Normal University,Shenyang 110034,China)

LetEbe a real Banach space with a uniformly Gǎteaux differentiable norm,Dbe a nonempty closed convex subset ofE.For the asymptotically nonexpansive mappingTwith sequence,under a certain condition,Zhao and Zhang proved that the Ishikawa iteration sequence ofTwith errors converges strongly to the fixed point ofT.It was proved that this result is also true for the general asymptotically nonexpansive mapping.

asymptotically nonexpansive mapping;Ishikawa iteration sequence;converge;fixed point

O 177.91

A

1008-9225(2010)01-0008-03

2009-07-09

程从沈(1957-),男,四川隆昌人,沈阳大学副教授·

【责任编辑 李 艳】