關(guān)于漸近非擴(kuò)張映象不動(dòng)點(diǎn)的一個(gè)注記

程從沈,程叢電

(1.沈陽(yáng)大學(xué) 理學(xué)院,遼寧 沈陽(yáng) 110041;2.沈陽(yáng)師范大學(xué) 數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院,遼寧 沈陽(yáng) 110034)

關(guān)于漸近非擴(kuò)張映象不動(dòng)點(diǎn)的一個(gè)注記

程從沈1,程叢電2

(1.沈陽(yáng)大學(xué) 理學(xué)院,遼寧 沈陽(yáng) 110041;2.沈陽(yáng)師范大學(xué) 數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院,遼寧 沈陽(yáng) 110034)

設(shè)E是具一致 Gǎteaux可微范數(shù)的實(shí)Banach空間,D是E的一個(gè)凸子集·對(duì)于序列{kn}?[0,∞)的漸近非擴(kuò)張映象T,趙良才和張石生在一定條件下給出并證明了關(guān)于T的具誤差的Ishikawa迭代序列收斂于T的不動(dòng)點(diǎn)·證明了這一結(jié)論對(duì)于一般的漸近非擴(kuò)張映象也是成立的·

漸近非擴(kuò)張映象;Ishikawa迭代序列;收斂;不動(dòng)點(diǎn)

[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] 趙良才,張石生·Banach空間中漸進(jìn)非擴(kuò)張型映象具誤差的強(qiáng)收斂定理[J]·數(shù)學(xué)學(xué)報(bào),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

程從沈(1957-),男,四川隆昌人,沈陽(yáng)大學(xué)副教授·

【責(zé)任編輯 李 艷】