留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

非Archimedean随机空间中混合型泛函方程的解及稳定性

张石生 R·萨达提 G·萨德基

张石生, R·萨达提, G·萨德基. 非Archimedean随机空间中混合型泛函方程的解及稳定性[J]. 应用数学和力学, 2011, 32(5): 623-634. doi: 10.3879/j.issn.1000-0887.2011.05.012
引用本文: 张石生, R·萨达提, G·萨德基. 非Archimedean随机空间中混合型泛函方程的解及稳定性[J]. 应用数学和力学, 2011, 32(5): 623-634. doi: 10.3879/j.issn.1000-0887.2011.05.012
ZHANG Shi-sheng, R. Saadati, G. Sadeghi. Solution and Stability of a Mixed Type Functional Equation in Non-Archimedean Random Spaces[J]. Applied Mathematics and Mechanics, 2011, 32(5): 623-634. doi: 10.3879/j.issn.1000-0887.2011.05.012
Citation: ZHANG Shi-sheng, R. Saadati, G. Sadeghi. Solution and Stability of a Mixed Type Functional Equation in Non-Archimedean Random Spaces[J]. Applied Mathematics and Mechanics, 2011, 32(5): 623-634. doi: 10.3879/j.issn.1000-0887.2011.05.012

非Archimedean随机空间中混合型泛函方程的解及稳定性

doi: 10.3879/j.issn.1000-0887.2011.05.012
详细信息
    作者简介:

    张石生(1934-),男,云南曲靖人,教授(E-mail:changss@yahoo.cn);R. Saadati,教授,博士(联系人.E-mail:rsaadati@eml.cc).

  • 中图分类号: O177.91

Solution and Stability of a Mixed Type Functional Equation in Non-Archimedean Random Spaces

  • 摘要: 在非-Archimedean 随机赋范空间的框架下,证明了Euler-Lagrange二次映象的广义稳定性.另外,文中还介绍了 随机空间理论、非-Archimedean 空间理论、以及泛函方程理论之间的联系.
  • [1] Forti G L. Hyers-Ulam stability of functional equations in several variables[J].Aequationes Math, 1995, 50(1/2): 143-190. doi: 10.1007/BF01831117
    [2] Hyers D H, Rassias Th M. Approximate homomorphisms[J].Aequationes Mathematics, 1992, 44(2/3): 125-153. doi: 10.1007/BF01830975
    [3] Rassias Th M. On the stability of functional equations and a problem of Ulam[J].Acta Appl Math, 2000, 62(1): 23-130. doi: 10.1023/A:1006499223572
    [4] Czerwik S. Stability of Functional Equations of Ulam-Hyers-Rassias Type[M].Florida: Hadronic Press, 2003.
    [5] Hyers D H, Isac G, Rassias Th M. Stability of Functional Equations in Several Variables[M].Basel: Birkhuser Verlag, 1998.
    [6] Jung S M. Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis[M].Florida: Hadronic Press, Inc, 2001.
    [7] Rassias Th M. Functional Equations, Inequalities and Applications[M].Dordrecht, Boston and London: Kluwer Academic Publishers, 2003.
    [8] Alsina C. On the stability of a functional equation arising in probabilistic normed spaces[J].General Inequalities. Vol 5.Basel: Birkhuser Verlag, 1987: 263-271.
    [9] Mirmostafaee M, Mirzavaziri M, Moslehian M S. Fuzzy stability of the Jensen functional equation[J]. Fuzzy Sets and Systems, 2008, 159(6): 730-738. doi: 10.1016/j.fss.2007.07.011
    [10] Mirzavaziri M, Moslehian M S.A fixed point approach to stability of a quadratic equation[J]. Bulletin of the Brazilian Mathematical Society, 2006, 37(3): 361-376. doi: 10.1007/s00574-006-0016-z
    [11] Mihe D, Radu D.On the stability of the additive Cauchy functional equation in random normed spaces[J]. Journal of Mathematical Analysis and Applications, 2008, 343(1): 567-572. doi: 10.1016/j.jmaa.2008.01.100
    [12] MiheD, Saadati R, Vaezpour S M. The stability of the quartic functional equation in random normed spaces[J]. Acta Applicandae Mathematicae, 2010, 110(2):797-793. doi: 10.1007/s10440-009-9476-7
    [13] Baktash E, Cho Y J, Jalili M, Saadati R, Vaezpour S M. On the stability of cubic mappings and quadratic mappings in random normed spaces[J]. J Inequal Appl, 2008. Article ID: 902187.doi: 10.1155/208/902187.
    [14] Saadati R, Vaezpour S M, Cho Y J. A note on the “On the stability of cubic mappings and quadratic mappings in random normed spaces” [J]. J Inequal Appl, 2009. Article ID: 214530, 6 pages.
    [15] 张石生, J.M.拉斯尔斯, R.沙达提. 直观随机赋范空间中三次泛函方程的稳定性[J].应用数学和力学, 2010, 31(1): 19-25.(ZHANG Shi-sheng, John Michael Rassias, Reza Saadati.The stability of a cubic functional equation in intuitionistic random normed spaces[J]. Applied Mathematics and Mechanics(English Edition),2010, 31(1): 21-26.)
    [16] Mohamadi M, Cho Y J, Park C, Vetro P, Saadati R. Random stability of an additive-quadratic-quartic functional equation[J]. J Inequal Appl, 2010. Article ID 754210, 18 pages, doi: 10.1155/2010/754210.
    [17] Eshaghi-Gordji M, Abbaszadeh S, Park C. On the stability of a generalized quadratic and quartic type functional equation in quasi-Banach spaces[J]. J Inequal Appl, Vol 2009. Article ID 153084, 26 pages, 2009.doi.10.1155/2009/153084.
    [18] Cho Y J, Park C, Saadati R. Functional inequalities in non-Archimedean Banach spaces[J]. Applied Mathematics Letters, 2010, 23(10): 1238-1242. doi: 10.1016/j.aml.2010.06.005
    [19] Saadati R, Park C. Non-Archimedean L-fuzzy normed spaces and stability of functional equations[J]. Computers and Mathematics With Applications, 2010, 60(8): 2488-2496. doi: 10.1016/j.camwa.2010.08.055
    [20] Saadati R, Cho Y J, Vahidi J. The stability of the quartic functional equation in various spaces[J]. Computers and Mathematics With Applications, 2010, 60(7): 1994-2002. doi: 10.1016/j.camwa.2010.07.034
    [21] Chang S S, Cho Y J, Kang S M. Nonlinear Operator Theory in Probabilistic Metric Spaces[M].New York: Nova Science Publishers, Inc, 2001.
    [22] Schweizer B, Sklar A. Probabilistic Metric Spaces[M].North Holand,New York: Elsevier, 1983.
    [23] erstnev A N. On the notion of a random normed space[J]. Dokl Akad Nauk SSSR, 1963, 142(2): 280-283.(in Russian).
    [24] Hadic' O, Pap E. Fixed Point Theory in PM-Spaces[M]. Dordrecht: Kluwer Academic Publishers, 2001.
    [25] Hadic' O, Pap E, Budincevic' M. Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces[J].Kybernetica, 2002, 38(3): 363-381.
    [26] Hensel K. Uber eine neue Begrundung der theorie der algebraischen Zahlen Jahres[J]. Deutsch Math Verein, 1897, 6: 8388.
    [27] Arriola L M, Beyer W A. Stability of the Cauchy functional equation over p-adic fields[J]. Real Anal Exchange, 2005, 31(1): 125-132.
    [28] Moslehian M S, Rassias Th M. Stability of functional equations in non-Archimedian spaces[J].Appl Anal Disc Math, 2007, 1(2): 325-334. doi: 10.2298/AADM0702325M
    [29] Moslehian M S, Sadeghi Gh. Stability of tow type of cubic functional equations in non-Archimedian spaces[J]. Real Anal Exchange, 2008, 33(2): 375-383.
    [30] Kim H M, Rassias J M. Generalization of the Ulam stability problem for Euler-Lagrange quadratic mapping[J]. Journal of Mathematical Analysis and Applications, 2007, 336(1): 277-296. doi: 10.1016/j.jmaa.2007.02.075
    [31] Mirmostafaee M, Moslehian M S.Fuzzy stability of additive mappings in non-Archimedean fuzzy normed spaces[J]. Fuzzy Sets and Systems, 2009, 160(11): 1643-1652. doi: 10.1016/j.fss.2008.10.011
  • 加载中
计量
  • 文章访问数:  1562
  • HTML全文浏览量:  131
  • PDF下载量:  806
  • 被引次数: 0
出版历程
  • 收稿日期:  2011-01-11
  • 修回日期:  2011-03-14
  • 刊出日期:  2011-05-15

目录

    /

    返回文章
    返回