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四次方程的广义Hyers-Ulam-Rassias稳定性 被引量：2

The generalized Hyers-Ulam-Rassias stability of quartic equations
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摘要 用不动点的择一性研究了四次方程的广义Hyers-Ulam-Rassias稳定性.证明了如果映射f:X→Y满足f(0)=0,‖(Df)(x,y)‖≤φ(x,y)(x,y∈X)且■0≤L<1,使得映射x|ψ(x):=φ(x/2,0)满足ψ(x)≤L24ψ(x/2)(x∈X),则存在惟一的四次映射V:X→Y,使得‖f(x)-V(x)‖≤(L/(2(1-L)))ψ(x)(x∈X). The generalized Hyers-Ulam-Rassias stability for quartic equation is investigated by using the fixed point alternative. It is proved that if a mapping f：X→Y satisfies f（0）=0, ｜｜ （Df）（x,y） ｜｜ 〈φ（x,y） （arbitary x,y ∈ X） and there exists a constant 0≤L〈1 such that φ（x）. =φ（x/2,0）≤L2^4 φ（x/2） （ arbitary x∈ X）,then there exists an unique quartic mapping V：X→Y such that｜｜ f（x）-g（x） ｜｜ ≤（L/（2（1-L））） φ （x） （ arbitary x∈ X）.
作者 郑文婷 曹怀信
机构地区 陕西师范大学数学与信息科学学院
出处 《纺织高校基础科学学报》 CAS 2008年第1期55-57,共3页 Basic Sciences Journal of Textile Universities
基金 国家自然科学基金资助项目(10571113)
关键词 Hyers-Ulam—Rassias稳定性 四次方程 不动点的择一性 Hyers-Ulam-Rassias stability quartic equation fixed point alternative
分类号 O177.1 [理学—基础数学]
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参考文献12

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同被引文献11

  • 1ULAM S M. A Collection of the mathematical prohlems[MJ. New Yorks Inter-Science Press, 1960.
  • 2HYERS D H. On the stability of the linear functional equation[J]. Proc Nat Acad Sci, 1941,27,222-224.
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  • 8GAO Z X,CAO H X,ZHENG W T ,et al, Generalized Hyers-Ulam-Rassias stability of functional inequalities and func?tional equations[J].J Math Inequal,2009,3: 63-77.
  • 9CAD H X,LVJ R,RASSIASJ M. Superstability for generalized module left derivations and generalized module deri?vations on a banach module (I)[J].J of Inequalities and Applications, 2009 , 10.1155/2009/718020,1-10.
  • 10CAD H X,LVJ R,RASSIASJ M. Superstability for generalized module left derivations and generalized module deri?vations on a Banach module(lI)[J].J Pure Appl Math,2009,10, 1-8.

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纺织高校基础科学学报
2008年 第1期

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