The superstability of a variant of Wilson’s functional equation on an arbitrary group

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• 作者：D. Zeglami
• 关键词：Superstability ; Wilson’s functional equation ; Pexider ; d’Alembert’s equation ; Primary 39B72 ; 39B32
• 刊名：Afrika Matematika
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：26
• 期：3-4
• 页码：609-617
• 全文大小：380 KB
• 参考文献：1.Badora, R.: On Hyers-Ulam stability of Wilson’s functional equation. Aequ. Math. 60, 211-18 (2000)View Article MATH MathSciNet
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  4.Bouikhalene, B., Elqorachi, E., Rassias, J.M.: The superstability of d’Alembert’s functional equation on the Heisenberg group. Appl. Math. Lett. 23(1), 105-09 (2010)View Article MATH MathSciNet
  5.C?dariu, L., Moslehian, M., Radu, V.: An application of Banach’s fixed point theorem to the stability of a general functional equation. An. Univ. Vest Timi?. Ser. Mat. Inform. 47(3), 21-6 (2009)MATH
  6.Davison, T.M.K.: D’Alembert’s functional equation on topological monoids. Publ. Math. Debr. 75(1-), 41-6 (2009)MATH MathSciNet
  7.Fechner, Z.: Wilson’s functional equation in algebras. Studia Sci. Math. Hung. 47(3), 388-00 (2010)MATH MathSciNet
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  10.Jung, S.: Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis. Springer Optimization and Its Applications. Springer, New York (2011). ISBN 978-1-4419-9636-7
  11.Kannappan, Pl, Kim, G.H.: On the stability of the generalized cosine functional equations. Ann. Acad. Pedag. Crac. Stud. Math. 1, 49-8 (2001)
  12.Kim, G.H.: The stability of pexiderized cosine functional equations. Korean J. Math. 16(1), 103-14 (2008)View Article
  13.Rassias, ThM: On the stability of linear mapping in Banach spaces. Proc. Am. Math. Soc. 72, 297-00 (1978)View Article MATH
  14.Redouani, A., Elqorachi, E., Rassias, ThM: The superstability of d’Alembert’s functional equation on step 2 nilpotent groups. Aequ. Math. 74(3), 237-48 (2007)View Article MathSciNet
  15.Roukbi, A., Zeglami, D., Kabbaj, S.: Hyers-Ulam stability of Wilson’s functional equation. Math. Sci. Adv. Appl. 22, 19-6 (2013)
  16.Stetk?r, H.: On a variant of Wilson’s functional equation on groups. Aequ. Math. 68(3), 160-76 (2004)View Article MATH
  17.Stetk?r, H.: Functionals Equations on Groups. World Scientific Publishing Company, Singapore (2013)View Article
  18.Székelyhidi, L.: On a stability theorem. C. R. Math. Rep. Acad. Sci. Can. 3, 253-55 (1981)MATH
  19.Székelyhidi, L.: D’Alembert’s functional equation on compact groups. Banach J. Math. Anal. 1(2), 221-26 (2007)View Article MATH MathSciNet
  20.Ulam, S.M.: A Collection of Mathematical Problems, Interscience Publishers New York, : Problems in Modern Mathematics. Wiley, New York (1961). 1964
  21.Zeglami, D. Roukbi, A., Kabbaj, S.: Hyers-Ulam stability of generalized Wilson’s and d’Alembert’s functional equations, Afr. Mat. (2013). doi:10.-007/?s13370-013-0199-6
  22.Zeglami, D., Kabbaj, S., Roukbi, A.: Superstability of a generalization of the cosine equation. Br. J. Math. Comput. Sci. 4(5), 719-34 (2014)View Article
  23.Zeglami, D., Kabbaj, S., Charifi, A., Roukbi, A.: \(\mu \) -Trigonometric functional equations and Hyers-Ulam stability problem in hypergroups. Functional Equations in Mathematical Analysis. Springer Optimization and Its Applications, vol. 52 (2012). doi:10.-007/-78-1-4614-0055-426
  
• 作者单位：D. Zeglami (1)
  
  1. Department of Mathematics, Faculty of Sciences, IBN Tofail University, BP: 14000, Kenitra, Morocco
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics Education
  Applications of Mathematics
  History of Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2190-7668

文摘

The aim of this paper is to investigate the superstability problem for the variant $$\begin{aligned} f(xy)+f(\sigma (y)x)=2f(x)g(y),\ \ \ \ x,y\in G, \end{aligned}$$