一致Banach空间中非扩张映象的弱收敛定理

Abstract

Abstract:

设犈是一致凸Ｂａｎａｃｈ空间，满足Ｏｐｉａｌ条件或具有Ｆｒｅｃｈｅｔ可微范数，犆是犈的非空闭凸子集，且犜：犆→犆是非扩张映象．又设对任何初始数据狓１ ∈犆，序列｛狓狀｝由下列修改了的Ｉｓｈｉｋａｗａ迭代程序生成：狓狀＋１＝狋狀犜狀（狊狀犜狀狓狀＋（１－狊狀）狓狀）＋（１－狋狀）狓狀，　狀≥１，（Ｉ）其中，数列｛狋狀｝与｛狊狀｝满足下列条件（ｉ）和（ｉｉ）之一：（ｉ）狋狀∈ ［犪，犫］且狊狀∈ ［０，犫］；（ｉｉ）狋狀∈ ［犪，１］且狊狀∈ ［犪，犫］，这里，常数犪，犫满足０＜犪≤犫＜１．作者证明了，犜有不动点的充要条件是，｛狓狀｝
弱收敛且｛‖狓狀－犜狓狀‖｝收敛到０．而且，由此即知，若犜有不动点，则｛狓狀｝弱收敛到犜的一个不动点．

Key words: 不动点；非扩张映象；修改了的Ｉｓｈｉｋａｗａ迭代程序；一致凸Ｂａｎａｃｈ空间；Ｏｐｉａｌ条件

CLC Number:

47H09

CENG Liu-Chuan. 一致Banach空间中非扩张映象的弱收敛定理[J].Acta mathematica scientia,Series A, 2002, 22(3): 336-341.

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References

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［１０］　ＳｃｈｕＪ．Ｉｔｅｒａｔｉｖｅｃｏｎｓｔｒｕｃｔｉｏｎｏｆｆｉｘｅｄｐｏｉｎｔｓｏｆａｓｙｍｐｔｏｔｉｃａｌｌｙｎｏｎｅｘｐａｎｓｉｖｅｍａｐｐｉｎｇｓ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９９１，１５８：４０７－４１３
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