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Altman型不动点定理 被引量：2

On the Theorems of Altman-type Fixed Point
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摘要 针对Altman型不动点定理,讨论了在第一个指数在0和1之间和第二个指数不大于0,以及只有一个小于0指数情形范数不等式条件下全连续算子不动点的存在性.证明了几个新的不动点定理.对应最近文献中第一个指数大于1,第二个指数不小于0在范数不等式条件下的不动点定理,推广和补充了这些文献中的结果. The theorems of Ahman-type fixed point are studied. The existence of the fixed point of completely continuous operator is discussed under the norm inequality conditions that the first exponent is between 0 and 1, the second one is not greater than 0 and there is only one exponent that is less than O. Some new fixed point theorems are proved. In contrast to the fixed point theorems as shown in earlier works where the first exponent is greater than 1 and the second one is not less than 0 under the norm inequality conditions, some supplements are given to those theorems.
作者 张国伟 山珊
机构地区 东北大学理学院
出处 《东北大学学报（自然科学版）》 EI CAS CSCD 北大核心 2009年第12期1800-1802,共3页 Journal of Northeastern University(Natural Science)
基金 国家自然科学基金资助项目(10771031)
关键词 不动点 全连续算子 1-集压缩 fixed point completely continuous operator 1-set-contractive
分类号 O177.91 [理学—基础数学]
  • 相关文献

参考文献11

  • 1孙经先.非线性泛函分析及其应用[M].北京:科学出版社.2007.
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  • 5张国伟,孙经先,张铁.凸泛函型的区域压缩与拉伸不动点定理[J].数学学报（中文版）,2008,51(3):517-522. 被引量：4
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  • 9Xu S Y. New fixed point theorems for 1-set-contractive operators in Banach spaces[J ]. Nonlinear Anal, 2007, 67 (3) :938 - 944.
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二级参考文献9

  • 1Dugundji J., An extension of Tietze theorem, Pacific J. Math., 1951, 1(3): 353-367.
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  • 9Taylor A. E., Lay D. C., Introduction to functional analysis (2th Edition), New York: John Wiley & Sons, 1980.

共引文献25

同被引文献11

  • 1孙经先,张晓燕.凸幂凝聚算子的不动点定理及其对抽象半线性发展方程的应用[J].数学学报（中文版）,2005,48(3):439-446. 被引量：19
  • 2孙经先.非线性泛函分析及其应用[M].北京:科学出版社.2007.
  • 3Granas A, Dugundji J. Fixed point theory [ M]. New York: Springer-Verlag, 2003.
  • 4Zhang G W, Zhang T S, Zhang T. Fixed point theorems of Rothe and Altman types about convex-power condensing operator and application [J].Applied Mathematics and Computation,2009,214 ( 2 ) : 618 - 623.
  • 5Zhao L H Z, Sun J X. Fixed point theorems of convex-power 1-set contraction operators in Banach spaces [ J ]. Fixed Point Theory and Applications,2012,56 : 1 - 8.
  • 6Xu S Y. New fixed point theorems for 1-set-contractive operators in Banach spaces [ J ]. Nonlinear Analysis, 2007,67 (3) :938 -944.
  • 7XU Shaoyuan. New fixed point theorems for 1-set-contractive operators in Banach spaces [J]. Nonlinear Anal, 2007, 67 (3) : 938-944.
  • 8ZHANG Guowei, ZHANG Tongshan, ZHANG Tie. Fixed point theorems of Rothe and Altman types about convex-power con- densing operator and application[J] Applied Mathematics and Computation, 2009, 214(2) :618-623.
  • 9SHI Hongbo, LI Wantong, SUN Hongrui, Existence of mild solutions for abstract mixed type semilinear evolution equations[J]. Turkish J Math, 2011, 35(3) :457-472.
  • 10ZHAO Lvhuizi, SUN Jingxian. Fixed point theorems of convex-power 1-setcontraction operators in Banach spaces [J].Fixed Point Theory and Applications, 2012, 2012(56) :1-8.

引证文献2

东北大学学报（自然科学版）
2009年 第12期

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