Czasopismo
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
We deal with mappings which preserve unit (some positive) distance, as well as with mappings contracting (expanding) some distance. In particular, we show that a mapping preserving three positive distances is an isometry.
Rocznik
Tom
Strony
10-14
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
autor
- Pedagogical Faculty Catholic Unwersity in Ružomberok Place A. Hlinka 56, 034 01 Ružomberok, Slovakia, billich@fedu.ku.sk
Bibliografia
- [1] F.S. Beckman, D.A. Quarles. On isometries of Euclidean spaces. Proc. Amer. Math. Soc. 4, 810 815, 1953.
- [2] W. Benz. Real Geometries. BI Wissenschaftsverlag, Mannheim-Leipzig-Wien-Zurich 1994.
- [3] W. Benz. Isometrien in normierten Räumen. Aequationes Math. 29, 204-209, 1985.
- [4] W. Benz, H. Berens. A contribution to a theorem of Ulam and Mazur. Aequationes Math. 34, Cl 63. 1987.
- [5] M. Billich. Zobrazenia zachovávajuce vzdialenost'. Acta Fac. Paed. Univ. Tyrnaviensis, Ser. C, No. 9, 18 22, 2005.
- [6] K. Ciesielski, Th.M. Rassias. On some properties of isometric mappings. Facta Univ. Math. Inform. 7, 107 115, 1992.
- [7] Th.M. Rassias. Is a distance one presserving mappings between metric spaces always an isometry? Amer. Math. Monthly 90, 200, 1983.
- [8] Th.M. Rassias. Some remarks on isometric mappings. Facta Univ. Ser. Math. Inform. 2, 49 52, 1087.
- [9] Th.M. Rassias. Mappings that preserves unit distance. Indian J. Math. 32, 275 278, 1990.
- [10] Th.M. Rassias. Isometric mappings and the problem of A.D. Aleksandrov for conservative distance. Proc. Intern. Graz Workshop, World Scientific, Singapore, pp. 118-125, 2001.
- [11] Th.M. Rassias, P. Šemrl. On the Mazur-Ulam theorem and the Alexandrov problem for unit distance preserving mappings. Proc. Amer. Math. Soc. 118, 919 925, 1993.
- [12] S. Xiang, Th.M. Rassias. On mappings with conservative distances and the Mazur-Ulam theorem. Univ. Beograd. Publ. Elektrotehn. Fak., Ser. Mat. 11, 1-8, 2000.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-68448e5c-1dff-43e5-87c3-5f5c789cc866