Stability of functional equations in \((n,\beta)\) -normed spaces

详细信息    查看全文

• 作者：Xiuzhong Yang (1) (2)
  Lidan Chang (1) (2)
  Guofen Liu (1) (2)
  Guannan Shen (1) (2)
  
  1. College of Mathematics and Information Science ; Hebei Normal University ; Shijiazhuang ; 050024 ; People鈥檚 Republic of China
  2. Hebei Key Laboratory of Computational Mathematics and Applications ; Shijiazhuang ; 050024 ; People鈥檚 Republic of China
  
• 关键词：39B82 ; 39B72 ; ( n ; 尾 ) $(n ; \beta)$ ; normed spaces ; non ; Archimedean ( n ; 尾 ) $(n ; \beta)$ ; normed space ; Cauchy functional equation ; Jensen functional equation ; pexiderized Cauchy functional equation
• 刊名：Journal of Inequalities and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,111 KB
• 参考文献：1. Ulam, SM (1960) A Collection of the Mathematical Problems. Interscience, 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. Rassias, TM (1978) On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 72: pp. 297-300 CrossRef
  4. Najati, A (2008) On the stability of a quartic functional equation. J. Math. Anal. Appl. 340: pp. 569-574 CrossRef
  5. Jung, SM (2011) Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis. Springer, New York
  6. Moslehian, MS, Rassias, TM (2007) Orthogonal stability of additive type equations. Aequ. Math. 73: pp. 249-259 CrossRef
  7. Radu, V (2003) The fixed point alternative and the stability of functional equations. Fixed Point Theory 4: pp. 91-96
  8. Mihet, D, Radu, V (2008) On the stability of the additive Cauchy functional equation in random normed spaces. J. Math. Anal. Appl. 343: pp. 567-572 CrossRef
  9. Saadati, R, Park, C (2010) Non-Archimedean L-fuzzy normed spaces and stability of functional equations. Comput. Math. Appl. 60: pp. 2488-2496 CrossRef
  10. Mirzavaziri, M, Moslehian, MS (2006) A fixed point approach to stability of a quadratic equation. Bull. Braz. Math. Soc. 37: pp. 361-376 CrossRef
  11. Park, C, Cho, YJ, Kenary, HA (2012) Orthogonal stability of a generalized quadratic functional equation in non-Archimedean spaces. J. Comput. Anal. Appl. 14: pp. 526-535
  12. G盲hler, S (1965) Lineare 2-normierte R盲ume. Math. Nachr. 28: pp. 1-43 CrossRef
  13. G盲hler, S (1969) Untersuchungen 眉ber Verallgemeinerte m-metrische R盲ume I. Math. Nachr. 40: pp. 165-189 CrossRef
  14. Kim, SS, Cho, YJ (1996) Strict convexity in linear n-normed spaces. Demonstr. Math. 29: pp. 739-744
  15. Malceski, R (1997) Strong n-convex n-normed spaces. Mat. Bilt. 21: pp. 81-102
  16. Misiak, A (1989) N-Inner product spaces. Math. Nachr. 140: pp. 299-319 CrossRef
  17. Gunawan, H, Mashadi, M (2001) On n-normed spaces. Int. J. Math. Math. Sci. 27: pp. 631-639 CrossRef
  18. Park, WG (2011) Approximate additive mappings in 2-Banach spaces and related topics. J. Math. Anal. Appl. 376: pp. 193-202 CrossRef
  19. Xu, TZ, Rassias, JM (2012) On the Hyers-Ulam stability of a general mixed additive and cubic functional equation in n-Banach spaces. Abstr. Appl. Anal. 2012:
  20. Xu, TZ (2013) Approximate multi-Jensen, multi-Euler-Lagrange additive and quadratic mappings in n-Banach spaces. Abstr. Appl. Anal. 2013:
  21. Hensel, K (1897) 脺ber eine neue Begr眉ndung der Theorie der algebraischen Zahlen. Jahresber. Dtsch. Math.-Ver. 6: pp. 83-88
  22. Katsaras, AK, Beoyiannis, A (1999) Tensor products of non-Archimedean weighted spaces of continuous functions. Georgian Math. J. 6: pp. 33-44 CrossRef
  23. Khrennikov, A (1997) Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models. Kluwer Academic, Dordrecht CrossRef
  24. Nyikos, PJ (1999) On some non-Archimedean spaces of Alexandroff and Urysohn. Topol. Appl. 91: pp. 1-23 CrossRef
  25. Moslehian, MS, Sadeghi, G (2008) A Mazur-Ulam theorem in non-Archimedean normed spaces. Nonlinear Anal. TMA 69: pp. 3405-3408 CrossRef
  
• 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 first introduce the notions of \((n,\beta)\) -normed space and non-Archimedean \((n,\beta)\) -normed space, then we study the Hyers-Ulam stability of the Cauchy functional equation and the Jensen functional equation in non-Archimedean \((n,\beta)\) -normed spaces and that of the pexiderized Cauchy functional equation in \((n,\beta)\) -normed spaces.