과제정보
연구 과제 주관 기관 : Ferdowsi University of Mashhad
참고문헌
- A. D. Aleksandrov, Mappings of families of sets, Soviet Math. Dokl. 11 (1970), 376-380.
- C. Alsina, On the stability of a functional equation arising in probabilistic normed spaces, in: General Inequalities, vol. 5, Oberwolfach, 1986, Birkhuser, Basel, 1987, 263-271.
- J. A. Baker, Isometries in normed spaces, Amer. Math. Monthly 78 (1971), 655-658. https://doi.org/10.2307/2316577
- S. S. Chang, Y. J. Cho and S. M. Kang, Nonlinear Operator Theory in Probabilistic Metric Spaces, Nova Science Publishers, Inc., New York, 2001.
- Y. J. Cho, Paul C. S. Lin, S. S. Kim and A. Misiak, Theory of 2-Inner Product Spaces, Nova Science Publishers, Inc., New York, 2001.
- H. Y. Chu, On the Mazur-Ulam problem in linear 2-normed spaces, J. Math. Anal. Appl. 327 (2007), 1041-1045. https://doi.org/10.1016/j.jmaa.2006.04.053
- H. Y. Chu, C. G. Park and W. G. Park , The Aleksandrov problem in linear 2-normed spaces , J. Math. Anal. Appl. 289 (2004), 666-672. https://doi.org/10.1016/j.jmaa.2003.09.009
- G. Dolinar, Generalized stability of isometries, J. Math. Anal. Appl. 242 (2000), 39-56. https://doi.org/10.1006/jmaa.1999.6649
- R. W. Freese and Y. J. Cho, Geometry of Linear 2-Normed Spaces Nova Science Publishers, Inc., New York, 2001.
- J. Gevirtz, Stability of isometries on Banach spaces, Proc. Amer. Math. Soc. 89 (1983), 633-636. https://doi.org/10.1090/S0002-9939-1983-0718987-6
- I. Golet, On probabilistic 2-normed spaces, Novi Sad J. Math. 35 (2005), 95-102.
- I. Golet, On generalized probabilistic 2-normed spaces, Proceeding ofthe Inter- national Conference on Theory and Application of Mathemathics and Infor- mations ICTAMI (2005)- Alba Iulia, Romania.
- P. Gruber, Stability of isometries, Trans. Amer. Math. Soc. 245 (1978), 263-277. https://doi.org/10.1090/S0002-9947-1978-0511409-2
- D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
- Y. Ma, The Aleksandrov problem for unit distance preserving mapping, Acta Math. Sci. Ser. B Engl. Ed. 20 (2000), 359-364.
- S. Mazur and S. Ulam, Sur les transformation isometriques d'espaces vectoriels normes, C. R. Acad. Sci. Paris 194 (1932), 946-948.
- K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. USA 28 (1942), 535-537. https://doi.org/10.1073/pnas.28.12.535
- B. Mielnik and Th. M. Rassias, On the Aleksandrov problem of conservative distances, Proc. Amer. Math. Soc. 116 (1992), 1115-1118. https://doi.org/10.1090/S0002-9939-1992-1101989-3
- D. Mihet, V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl. 343 (2008), 567-572. https://doi.org/10.1016/j.jmaa.2008.01.100
- M. S. Moslehian and Gh. Sadeghi, A mazur-Ulam theorem in non-Archimedean normed spaces, Nonlinear Anal. 69 (2008), 3405-3408. https://doi.org/10.1016/j.na.2007.09.023
- Th. M. Rassias, Properties of isometric mappings, J. Math. Anal. Appl. 235 (1999), 108-121. https://doi.org/10.1006/jmaa.1999.6363
- Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), 123-130.
- Th. M. Rassias and P. Semrl, On the Mazur-Ulam theorem and the Aleksandrov problem for unit distance preserving mapping, Proc. Amer. Math. Soc. 114 (1992), 989-993. https://doi.org/10.1090/S0002-9939-1992-1059634-1
- Th. M. Rassias and S. Xiang, On Mazur-Ulam theorem and mappings which preserve distances, Nonlinear Funct. Anal. Appl. 5 (2000), 61-66.
- B. Schweizer and A. Sklar, Probabilistic Metric Spaces, Elsevier, North Holand, New York, 1983.
- A. N. Serstnev, On the notion of a random normed space, Dokl. Akad. Nauk SSSR 149 (1963), 280-283.
- S. M. Ulam, Problems in modern mathematics, Science Editions John Wiley and Sons, Inc., New York, 1964.
- S. Xiang, Mappings of conservative distances and the Mazur-Ulam theorem, J. Math. Anal. Appl. 254 (2001), 262-274. https://doi.org/10.1006/jmaa.2000.7276