Mappings preserving some distances

• Autorzy: Billich M.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

isometric system; mapping function; Euclidean spaces

PL

izometria; funkcja mapowania; przestrzenie Euclidesowe

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2008
• Tom: Vol. 13
• Strony: 10--14
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Billich M.

• Pedagogical Faculty Catholic Unwersity in Ružomberok Place A. Hlinka 56, 034 01 Ružomberok, Slovakia

Bibliografia

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• [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.