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非线性算子的几种稳定性 被引量：2

Several stabilities of nonlinear operators
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摘要 研究了非线性算子的几种稳定性.采用算子论方法,提出了算子的ε-稳定性、一致稳定性、强一致稳定性和弱稳定性的定义,在此基础上研究了这些稳定性的一些充分条件、必要条件和充要条件. The main purpose of this paper is to study several stabilities of nonlinear operators by using operator theoretic method. The definitions of ε-stability, uniform stability, strong uniform stability and weak stability of a nonlinear operator are given. Some sufficient, necessary, as well as necessary and sufficient conditions for these stabilities are obtained.
作者 高振霞 曹怀信
机构地区 陕西师范大学数学与信息科学学院
出处 《陕西师范大学学报（自然科学版）》 CAS CSCD 北大核心 2007年第4期19-22,共4页 Journal of Shaanxi Normal University：Natural Science Edition
基金 国家自然科学基金资助项目(10571113)
关键词 ε-稳定性 一致ε-稳定性 强一致稳定性 弱稳定性 非线性算子 ε-stability uniform stability strong uniform stability weak stability nonlinear operator
分类号 O177.1 [理学—基础数学]
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参考文献10

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同被引文献26

  • 1Gao Zhenxia, Cao Huiaxin, Zheng Wenting,et al. Gen- eralized Hyers Ulam Rassias stability of functional ine- qualities and functional equations[J]. Journal of Mathe- matical Inequalities, 2009, 3(1): 63-77.
  • 2Xu Lu, Cao Huaixin, Zheng Wenting, et al. Super-sta- bility and stability of the exponential equations[J]. Jour- nal of Mathematical Inequalities, 2010, 4 (1) : 37-44.
  • 3Fechner W. On a composite functional equation on A- belian groups [J]. Aequationes Mathematicae, 2009, 78:185-193.
  • 4Fechner W. Stability of a composite functional equation related to idempotent mappings[J]. Journal of Approx- imation Theory, 2011, 163:328-335.
  • 5Hyers D H. On the stability of the linear functional equation [J ]. Proceedings of the National Academy of Sciences of United States of America, 1941, 27(4):222-224.
  • 6Rassias T M. On the stability of the linear mapping in Banach spaces [ J ]. Proceedings of the American Mathematical Society, 1978, 72(2) :297-300.
  • 7Baker J. The stability of the cosine equation [J].Proceedings of the American Mathematical Society, 1980, 80(3) :411-416.
  • 8Gajda Z. On stability of additive mappings [J]. International Journal of Mathematics and Mathematical Sciences, 1991, 14(3):431-434.
  • 9Rassias T M, Semerl P. On the behavior of mappings which do not satisfy Hyers-Ulam stability [J]. Proceedings of the American Mathematical Society, 1992, 114(4) :989-993.
  • 10Gavruta P. A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings[J]. Journal of Mathematical Analysis and Applications, 1994, 184 (3)431-436.

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陕西师范大学学报（自然科学版）
2007年 第4期

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