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Hilbert空间中非扩张映射的新不动点定理 被引量：2

New Fixed Point Theorems of Nonexpansive Mappings in Hilbert Spaces
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摘要 利用非扩张映射的非线性二择一性质,得到了Hilbert空间中非扩张映射的若干新不动点定理,从而推广了著名的非扩张映射Altman定理、Roth定理和Petryshyn定理. By means of nonlinear alternative for nonexpansive mappings, some new fixed point theorems of contraction mappings are obtained. As a result, the famous Altman＇ s theorem, Roth＇ s theorem and Petryshyn theorem for such class of mappings are generalized.
作者 许绍元
机构地区 赣南师范学院数学与计算机学院
出处 《河北师范大学学报（自然科学版）》 CAS 北大核心 2007年第6期718-721,共4页 Journal of Hebei Normal University：Natural Science
基金 国家自然科学基金(10571185) 江西省自然科学基金(0611005)
关键词 非扩张映射 非线性二择一 不动点 HILBERT空间 nonexpansive mapping nonlinear alternative fixed point Hilbert space
分类号 O177.91 [理学—基础数学]
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参考文献8

  • 1GRANAS A, DUGUNDJ I J. Fixed Point Theory [ M ]. New York :Springer-verlag, 2003.54.
  • 2ZEIDLER E. Nonlinear Functional Analysis and Its Applications [ M]. New York :Springer-verlag, 1986.
  • 3BROWDER F E. Nonexpansive Nonlinear Operators in Banach Spaces [J ]. Proe NAS USA, 1965,54:1 041-1 044.
  • 4BRUCK R E. Properties of Fixed Point Sets of Nonexpansive Mappings [J ]. Trans Amer Math Soc, 1973,179 : 251-262.
  • 5BRUCK R E. A Common Fixed Point Theorem Commuting Family of Nonexpansive Mappings [ J ]. Pacific J Math, 1974,53: 59-71.
  • 6KIRK W A, YANEZ C M, SHIN S S. Asymptotically Nonexpansive Mappings [J ]. Nonliear Anal, 1998,33:1-12.
  • 7KIRK W A, YANEZ C M. Nonexpansive Mappings and Local Nonexpansive Mappings in Product Spaces [J ]. Nonliear Anal, 1988,12:719-725.
  • 8KIRK W A. Nonexpansive Mappings and Asymptotic Regularity [J ]. Nonliear Anal, 2000,40 : 323-332.

同被引文献10

  • 1Altman M.A fixed point theorem in Banach space[J].Bull Polish Acad Sci,1957,(5):19-22.
  • 2Dugundji,Granas.A fixed point theory[M].Warszawa:PwN-Polish Sci Pub,1982.
  • 3Granas A.Dugundj I J.Fixed point theory[M].New York:Springer-verlag,2003.
  • 4Browder F E.Nonexpansive nolinear operators in Banach spaces[J].Proc NAS USA,1965,54:1041-1044.
  • 5Zeidler E.Nonlinear functional analysis and its applications[M].New York:Springer-verlag,1986.
  • 6Kirk W A,Yanez C M.Nonexpansive mappings and local nonexpnsive mapping in product spaces[J].Nonliear Anal,1988,12:719-725.
  • 7Kirk W A,Yanez C M,Shin S S.Asymptotically Nonexpansive mappings[J].Nonliear Anal,1998,33:1-12.
  • 8Kirk W A.Nonexpansive mappings and asymptotic regularity[J].Nonliear Anal,2000,40:323-332.
  • 9Bruck R E.Properties of fixed point sets of nonexpansive mapping[J].Trans Amer Math Soc,1973,179:251-262.
  • 10Bruck R E.A common fixed point theorem commuting family of nonexpansive mappings[J].Pacific J Math,1974,53:59-71.

引证文献2

河北师范大学学报（自然科学版）
2007年 第6期

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