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Hilbert空间中非扩张映象不动点迭代逼近的CQ方法 被引量：1

The CQ Method for Iterative Approximation of Nonexpansive-Mapping Fixed Points in Hilbert Spaces
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摘要 在Hilbert空间中,利用CQ方法证明了非扩张映象的Halpern迭代序列是良定的,并证明了该迭代序列有界是非扩张映象不动点存在的一个充要条件.推广了Matsushita与Takahashi的某些结果。 By use of CQ method,the Halpern iterative sequences involving nonexpansive mappings have been proven well-defined.Proven also is the sufficient and necessary condition being that such Halpern iterative sequences must be bounded for the existence of fixed points of nonexpansive mappings in the Hilbert spaces.These results can serve to generalize some results of Matsushita and Takahashi.
作者 赵世莲
机构地区 西华师范大学数学与信息学院
出处 《内江师范学院学报》 2010年第8期14-16,43,共4页 Journal of Neijiang Normal University
基金 国家自然科学基金(60804065) 西华师范大学科研启动基金(08B075)资助
关键词 非扩张映象 不动点 CQ方法 Halpern迭代 nonexpansive mapping fixed point CQ method halpern iterative sequence
分类号 O177.91 [理学—基础数学]
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参考文献13

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二级参考文献53

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共引文献10

同被引文献13

  • 1Mann W R.Mean value methods in iteration[J].Proceedings of the American Mathematical Society,1953,(3):506-510.
  • 2Ishikawa S.Fixed points and iterations of non-expansive mappings in Banach spaces[J].Proceedings of the American Mathematical Society,1976,59 (1):65-71.
  • 3Genel A,Lindenstrauss J.An example concerning fixed points[J].ISRAEL Journal of Mathematics,1975 22(1):81-86.
  • 4Takahashi W.Nonlinear Functional Analysis[M].Yokohama:Yokohama Publishers,2000.
  • 5Nakajo K,Takahashi W.Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups[J].Mathematical Analysis and Applications,2003,279 (2):372-379.
  • 6Kim T H,Xu H K.Strong convergence of modified Mann iterations for asymptotically nonexpansive mapping and semigroups[J].Nonlinear Analysis,2006,64 (5):1140-1152.
  • 7Goebel K,Kirk W A.A fixed point theorems for asymp-totically nonexpansive mappings[J].Proceedings of the American Mathematical Society,1972,35(1):171-174.
  • 8Xu B L,Noor M A.Fixed-Point Iterations for Asymp-totically Nonexpansive Mappings in Banach Spaces[J].Journal of Mathematical Analysis and Applications,2002,267(2):444-453.
  • 9Lin P K,Tan K K,Xu H K.Demiclosedness principle and asymptotic behavior for asymptotically nonexpansive mappings[J].Nonlinear Analysis,1995,24(6):929-946.
  • 10Martinez-Yanes C,Xu H K.Strong convergence of the CQ method for fixed points iteration processes[J]Nonlinear Analysis,2006,64 (11):2400-2411.

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内江师范学院学报
2010年 第8期

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