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On distance-preserving mappings

Themistocles M. Rassias|Soon-Mo Jung
대한수학회 (The Korean Mathematical Society)|2004.07|대한수학회지 (Journal of the KMS)|제41권 제4호|pp. 667-680

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참고문헌

주제분류수학

초록

Abstract

We generalize a theorem of W. Benz by proving the following result: Let Hµ be a half space of a real Hilbert space with dimension ¸ 3 and let Y be a real normed space which is strictly convex. If a distance ½ > 0 is contractive and another distance N½ (N ¸ 2) is extensive by a mapping f : Hµ ! Y , then the restriction fjHµ+½=2 is an isometry, where Hµ+½=2 is also a half space which is a proper subset of Hµ. Applying the above result, we also generalize a classical theorem of Beckman and Quarles.

참고문헌 (19)

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  2. F. S. Beckman, "On isometries of Euclidean spaces", 4, pp.810~815 (1953)
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  4. "An elementary proof the orem of Beckman and Quarles", 42, pp.4~9 (1987)
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  10. "On a characteristic property of isometric mappings", 17, pp.43~45 (1976)
  11. "On the Aleksandrov problem of conservativedistances", 116, pp.1115~1118 (1992)
  12. "Some remarks on isometric mappings", 2, pp.49~52 (1987)
  13. "Mappings that preserve unit distance", 32, pp.275~278 (1990)
  14. "Properties of isometries and approximate isometries", pp.341~379 (1998)
  15. "Properties of isometric mappings", 235, pp.108~121 (1999)
  16. "Properties of isometries", 3, pp.1~38 (1993)
  17. "On the Mazur-Ulam theorem and the Aleksandrovproblem for unit distance preserving mapping", 118, pp.919~925 (1993)
  18. "Eine Erganzung zum Satz von Beckman and Quarles", 19, pp.89~92 (1979)
  19. "Congruence-preserving mappings", 43, pp.37~38 (1970)

관련 논문AI추천

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