| Hyers-Ulam-Rassias stability of approximate isometries on restricted domains |
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| 引用本文： | XIANG Shu huang College of Mathematical Science and Computational Technology,Central South University,Changsha 410083,China. Hyers-Ulam-Rassias stability of approximate isometries on restricted domains[J]. 中南工业大学学报(英文版), 2002, 9(4): 289-292. DOI: 10.1007/s11771-002-0044-9 |
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| 作者姓名： | XIANG Shu huang College of Mathematical Science and Computational Technology Central South University Changsha 410083 China |
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| 作者单位： | XIANG Shu huang College of Mathematical Science and Computational Technology，Central South University，Changsha 410083，China |
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| 基金项目： | TheScienceandArtFoundationofCentralSouthUniversity . |
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| 摘 要： | Let X and Y be real Banach spaces. The stability of Hyers-Ulam-Rassias approximate isometries on restricted domains S(unbounded or bounded) for into mapping f: S→Y satisfying ‖f(x)-f(y)‖-‖x-y‖≤ε(x,y) for all x,y∈S is studied in case that the target space Y is uniformly convex Banach space of the modulus of convexity of power type q≥2 or Y is the Lq(Ω,,μ) (1＜q＜ ∞) space or Y is a Hilbert space. Furthermore, the stability of approximate isometries for the case that (x,y)=‖x‖p ‖y‖p or (x,y)=‖x-y‖p for p≠1 is investigated.
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| 收稿时间： | 2002-02-20 |
Hyers-Ulam-Rassias stability of approximate isometries on restricted domains |
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| Xiang Shu-huang. Hyers-Ulam-Rassias stability of approximate isometries on restricted domains[J]. Journal of Central South University of Technology, 2002, 9(4): 289-292. DOI: 10.1007/s11771-002-0044-9 |
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| Authors: | Xiang Shu-huang |
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| Affiliation: | College of Mathematical Science and Computational Technology, Central South University, Changsha 410083, China |
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| Abstract: | Let X and Y be real Banach spaces. The stability of Hyers-Ulam-Rassias approximate isometries on restricted domains S (unbounded or bounded) for into mapping f: S → Y satisfying | ‖ f(x) − f(y) ‖ − ‖ x − y ‖ | ⩽ εφ (x, y) for all x, y ε S is studied in case that the target space Y is uniformly convex Banach space of the modulus of convexity of power type q ⩾ 2 or Y is the L q (Ω, Σ, μ) (1<q<+∞) space or Y is a Hilbert space. Furthermore, the stability of approximate isometries for the case that φ (x, y)=‖ x ‖ p + ‖ y p or φ(x, y)=‖ x − y ‖ p for p≠1 is investigated. Foundation item: The Science and Art Foundation of Central South University. Biography of the author: XIANG Shu-huang, doctor, professor, born in 1966, majoring in numerical analysis and functional analysis. |
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| Keywords: | Hyers-Ulam-Rassias stability isometry uniformly convex space Hilbert space |
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