On stability of functional equations related to quadratic mappings in fuzzy Banach spaces
详细信息    查看全文
  • 作者:Seong Sik Kim (23)
    Nawab Hussain (24)
    Yeol Je Cho (24) (25)

    23. Department of Mathematics
    ; Dongeui University ; Busan ; 614-714 ; Korea
    24. Department of Mathematics
    ; King Abdulaziz University ; Jeddah ; 21589 ; Saudi Arabia
    25. Department of Mathematics Education and the RINS
    ; Gyeongsang National University ; Chinju ; 660-701 ; Korea
  • 关键词:radical functional equations ; stability ; fuzzy Banach spaces
  • 刊名:Journal of Inequalities and Applications
  • 出版年:2014
  • 出版时间:December 2014
  • 年:2014
  • 卷:2014
  • 期:1
  • 全文大小:248 KB
  • 参考文献:1. Ulam, SM (1940) Science Editions. Problems in Modern Mathematics. Wiley, New York
    2. Hyers, DH (1941) On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27: pp. 222-224 CrossRef
    3. Aoki, T (1950) On the stability of the linear transformation in Banach spaces. J. Math. Soc. Jpn 2: pp. 64-66 CrossRef
    4. Rassias, TM (1978) On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc 72: pp. 297-300 CrossRef
    5. G菐vruta, P (1994) A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings. J. Math. Anal. Appl 184: pp. 431-436 CrossRef
    6. C膬dariu, L, Radu, V (2003) Fixed points and the stability of Jensen鈥檚 functional equation. J. Inequal. Pure Appl. Math.
    7. Skof, F (1983) Propriet脿 locali e approssimazione di operatori. Rend. Semin. Mat. Fis. Milano 53: pp. 113-129 CrossRef
    8. Gordji, ME, Khodaei, H, Ebadian, A, Kim, GH (2012) Nearly radical quadratic functional equations in p-2-normed spaces. Abstr. Appl. Anal.
    9. Gordji, ME, Parviz, M (2009) On the Hyers-Ulam stability of the functional equation. Nonlinear Funct. Anal. Appl 14: pp. 413-420
    10. Khodaei, H, Gordji, ME, Kim, SS, Cho, YJ (2012) Approximation of radical functional equations related to quadratic and quartic mappings. J. Math. Anal. Appl 395: pp. 284-297 CrossRef
    11. Kim, SS, Cho, YJ, Gordji, ME (2012) On the generalized Hyer-Ulam-Rassias stability problem on radical functional equations. J. Inequal. Appl.
    12. Katsaras, AK (1984) Fuzzy topological vector spaces II. Fuzzy Sets Syst 12: pp. 143-154 CrossRef
    13. Felbin, C (1992) Finite-dimensional fuzzy normed linear space. Fuzzy Sets Syst 48: pp. 239-248 CrossRef
    14. Kramosil, I, Mich谩lek, J (1975) Fuzzy metrics and statistical metric spaces. Kybernetika 11: pp. 336-344
    15. Krishna, SV, Sarma, KKM (1994) Separation of fuzzy normed linear spaces. Fuzzy Sets Syst 63: pp. 207-217 CrossRef
    16. Xiao, JZ, Zhu, XH (2003) Fuzzy normed space of operators and its completeness. Fuzzy Sets Syst 133: pp. 389-399 CrossRef
    17. Cheng, SC, Mordeson, JN (1994) Fuzzy linear operators and fuzzy normed linear spaces. Bull. Calcutta Math. Soc 86: pp. 429-436
    18. Bag, T, Samanta, SK (2003) Finite dimensional fuzzy normed linear spaces. J. Fuzzy Math 11: pp. 687-705
    19. Mihet, D (2010) The stability of additive Cauchy functional equation in non-Archimedean fuzzy normed spaces. Fuzzy Sets Syst 161: pp. 2206-2212 CrossRef
    20. Mirmostaface, AK (2012) Pertubation of generalized derivations in fuzzy Menger normed algebras. Fuzzy Sets Syst 195: pp. 109-117 CrossRef
    21. Mirmostafaee, AK, Moslehian, MS (2008) Fuzzy versions of Hyers-Ulam-Rassias theorem. Fuzzy Sets Syst 159: pp. 720-729 CrossRef
    22. Mirmostafaee, AK, Mirzavaziri, M, Moslehian, MS (2008) Fuzzy stability of the Jensen functional equation. Fuzzy Sets Syst 159: pp. 730-738 CrossRef
    23. Park, C (2009) Fuzzy stability of a functional equation associated with inner product spaces. Fuzzy Sets Syst 160: pp. 1632-1642 CrossRef
    24. Dias, JB, Margolis, B (1968) A fixed point theorem of the alternative for contractions on a generalized complete metric space. Bull. Am. Math. Soc 74: pp. 305-309 CrossRef
    25. C膬dariu, L, Radu, V (2004) On the stability of the Cauchy functional equation: a fixed point approach. Grazer Math. Ber 346: pp. 43-52
  • 刊物主题:Analysis; Applications of Mathematics; Mathematics, general;
  • 出版者:Springer International Publishing
  • ISSN:1029-242X
文摘
In this paper, we establish the generalized Hyers-Ulam stability problem of radical quadratic functional equations in fuzzy Banach spaces via the direct and fixed point methods. MSC: 39B72, 39B82, 39B52, 47H09.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700