Some remarks on mappings that preserve unit distance

• Autorzy: Billich M.
• Języki publikacji: EN

Abstrakty

EN

In the present paper we investigate some properties on isometric mappings between Euclidean spaces. In addition, non-isometric distance one preserving mappings are also considered.

Słowa kluczowe

EN

Euclidean space; vector space; mapping

PL

przestrzeń Euklidesa; przestrzeń euklidesowa; przestrzeń wektorowa; mapowanie

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2009
• Tom: Vol. 14
• Strony: 7--11
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Billich M.

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

Bibliografia

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• [3] B.V. Dekster. Non-isometric distance 1 preserving mapping E2→E 6.Arch. Math. ,45, 282–283, 1985.
• [4] A.V. Kuz’minykh. On a characteristic property of isometric mappings. Soviet Math. Dokl. ,17 , 43–45, 1976.
• [5] Th.M. Rassias. Is a distance one presserving mappings between metric spaces always an isometry? Amer. Math. Monthly ,90 , 200, 1983.
• [6] Th.M. Rassias. Some remarks on isometric mappings. Facta Univ. Ser.Math. Inform.,2, 49-52, 1987.
• [7] Th.M. Rassias. Properties of isometric mappings. J. Math. Anal. Appl. , 235 , 108–121, 1999.
• [8] 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.
• [9] Th.M. Rassias, C.S. Sharma. Properties of isometries. J. Natural Geom., 3 , No.1, 1-38, 1993.
• [10] 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