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Hyers-Ulam-Rassias stability of approximate isometries on restricted domains

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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 Lq (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 + ‖ yp or φ(x, y)=‖ x − y ‖ p for p≠1 is investigated.

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Authors and Affiliations

  1. College of Mathematical Science and Computational Technology, Central South University, 410083, Changsha, China

    Xiang Shu-huang

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  1. Xiang Shu-huang
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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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Xiang, Sh. Hyers-Ulam-Rassias stability of approximate isometries on restricted domains. J Cent. South Univ. Technol. 9, 289–292 (2002). https://doi.org/10.1007/s11771-002-0044-9

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  • DOI: https://doi.org/10.1007/s11771-002-0044-9

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