Browse > Article
http://dx.doi.org/10.4134/BKMS.2003.40.1.009

MAPPINGS OF CONSERVATIVE DISTANCES  

Jung, Soon-Mo (Mathematics Section, College Of Science And Technology, Hong-Ik University)
Publication Information
Bulletin of the Korean Mathematical Society / v.40, no.1, 2003 , pp. 9-15 More about this Journal
Abstract
In this paper, we will deal with the Aleksandrov-Rassias problem. More precisely, we prove some theorems concerning the mappings preserving one or two distances.
Keywords
Aleksandrov problem; Aleksandrov Rassias problem; isometry; distance preserving mapping;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Isometrien in normierten Rauman /
[ W. Benz ] / Aequationes Math.   DOI
2 Some remarks on isometric mappings /
[ Th. M. Rassias ] / Facta Univ. Ser. Math. Inform.
3 Is a distance one preserving mapping between metric spaces always on isometry? /
[ Th. M. Rassias ] / Amer. Math. Monthly   DOI   ScienceOn
4 Properties of isometries and approximate isometries /
[ Th. M. Rassias;G. V. Milovanovic(Edited) ] / Recent Progress in Inequalities
5 On some properties of isometric mappings /
[ K. Ciesielski;Th. M. Rassias ] / Facta Univ. Ser. Math. Inform.
6 On a characteristic property of isometric mappings /
[ A. V. Kuz'minyh ] / Soviet Math. Dokl.
7 Properties of isometric mappings /
[ Th. M. Rassias ] / J. Math. Anal. Appl.   DOI   ScienceOn
8 Functions that preserve unit distance /
[ D. Greenwell;P. D. Johnson ] / Math. Mag.   DOI
9 Properties of isometries /
[ Th. M. Rassias;C. S. Sharma ] / J. Natur. Geom.
10 Characterizing motions by unit distance invariance /
[ R. L. Bishop ] / Math. Mag.   DOI
11 Mappings of conservative distances and the Mazur-Ulam theorem /
[ S. Xiang ] / J. Math. Anal. Appl.   DOI   ScienceOn
12 A contribution to a theorem of Ulam and Mazur /
[ W. Benz;H. Berens ] / Aequationes Math.   DOI
13 On the Aleksandrov problem of conservative distances /
[ B. Mielnik;Th. M. Rassias ] / Proc. Amer. Math. Soc.   DOI   ScienceOn
14 On isometries of Euclidean spaces /
[ F. S. Beckman;D. A. Quarles ] / Proc. Amer. Math. Soc.   DOI   ScienceOn
15 Eine Erganzung zum Satz von Beckman and Quarles /
[ E. M. Schroder ] / Aequationes Math.   DOI
16 Mappings of conservative distances and the Mazur-Ulam theorem /
[ C. G. Townsend ] / J. Math. Anal. Appl.   DOI   ScienceOn
17 On mappings that preserve a family of sets in Hilbert and hyperbolic spaces /
[ A. Guc ] / Candidate's Dissertation
18 On the Mazur-Ulam theorem and the Aleksandrov problem for unit distance preserving mappings /
[ Th. M. Rassias;P. Semrl ] / Proc. Amer. Math. Soc.   DOI   ScienceOn
19 On Mazur-Ulam theorem and mappings which preserve distances /
[ Th. M. Rassias;S. Xiang ] / Nonlinear Funct. Anal. Appl.
20 On mappings with conservative distances and the Mazur-Ulam theorem /
[ Th. M. Rassias;S. Xiang ] / Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat.
21 Elementary proof of the theorem of Beckman and Quarles /
[ W. Benz ] / Elem. Math.
22 Mappings that preserve unit distance /
[ Th. M. Rassias ] / Indian J. Math.
23 Mapping of families of sets /
[ A. D. Aleksandrov ] / Soviet Math. Dokl.