ON MAPPINGS PRESERVING REGULAR POLYGONS

Byungbae Kim (Korea)

Received August 21, 2007; Revised January 18, 2008

References:

[1] A. D. Aleksandrov, Mapping of families of sets, Soviet Math. Dokl. 11 (1970), 116-120. [2] F. S. Beckman and D. A. Quarles, On isometries of Euclidean spaces, Proc. Amer. Math. Soc. 4 (1953), 810-815. [3] W. Benz, Isometrien in normierten Räumen, Aequationes Math. 29 (1985), 204-209. [4] S. M. Jung, Mappings preserving some geometrical figures, Acta Math. Hungar. 100 (2003), 167-175. [5] S. M. Jung, On mappings preserving pentagons, Acta Math. Hungar. 110 (2006), 261-266. [6] S. M. Jung and B. Kim, Unit-circle preserving mappings, Int. J. Math. Math. Sci. 66 (2004), 3577-3586. [7] S. M. Jung and B. Kim, Unit-sphere preserving mappings, Glasnik Math. 39(59) (2004), 327-330. [8] B. Mielnik and Th. M. Rassias, On the Aleksandrov problem of conservative distances, Proc. Amer. Math. Soc. 116 (1992), 1115-1118. [9] Th. M. Rassias, Is a distance one preserving mapping between metric spaces always an isometry? Amer. Math. Monthly 90 (1983), pp. 200. [10] Th. M. Rassias, Some remarks on isometric mappings, Facta Univ. Ser. Math. Inform. 2 (1987), 49-52. [11] C. G. Townsend, Congruence-preserving mappings, Math. Mag. 43 (1970), 37-38.

Keywords and phrases: isometry, polygon, polygon preserving mapping.