The superstability of d'Alembert's functional equation on step 2 nilpotent groups

被引：2
作者：
Redouani A. [1 ]
Elqorachi E. [1 ]
Rassias T.M. [2 ]
机构：
[1] Department of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir
[2] Department of Mathematics, National Technical University of Athens, Zografou Campus
来源：
Aequationes mathematicae | 2007年 / 74卷 / 3期
关键词：
D'Alembert's equation; Step 2 nilpotent groups; Superstability;
D O I：
10.1007/s00010-007-2902-x
中图分类号：
学科分类号：
摘要：
In the present paper we study the superstability of d'Alembert's functional equations f(xy) +f(xy{-1}) = 2f(x)f(y), x, y ∈ G, and f(xy) + f(yx) + f(xy{-1}) +f(y{-1}x) = 4f(x)f(y), x, y ∈ G, on any step 2 nilpotent group G. © 2007 Birkhäuser Verlag AG.
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页码：226 / 241
页数：15
相关论文
共 21 条
  • [1] BADORA R., On Hyers-Ulam stability of Wilson's functional equation, Aequationes Math, 60, pp. 211-218, (2000)
  • [2] BAKER J.A., The stability of the cosine equation, Proc. Amer. Math. Soc, 80, pp. 411-416, (1980)
  • [3] BAKER J., LAWRENCE J., ZORZITTO F., The stability of the equation f(x+y) = f(x)f(y), Proc. Amer. Math. Soc, 14, pp. 242-246, (1979)
  • [4] COROVEI I., The d'Alembert functional equation on metabelian groups, Aequationes Math, 57, pp. 201-205, (1999)
  • [5] COROVEI I., The functional equation f(xy) + f(yx) + f(xy<sup>-1</sup>) + f(y<sup>-1</sup>x) = 4f(x)f(y) for nilpotent groups, Cluj-Napoca Ser. Mat.-Fiz.-Mec. Appl, 20, pp. 25-28, (1977)
  • [6] ELQORACHI E., AKKOUCHI M., The superstability of the generalized d'Alembert functional equation, Georgian Math. J, 10, pp. 503-508, (2003)
  • [7] DE PLACE FRIIS P., D'Alembert's and Wilson's equations on Lie groups, Aequationes Math, 67, pp. 12-25, (2004)
  • [8] GER R., Superstability is not natural, Rocznik Nauk.-Dydakt. Prace Mat, 159, 13, pp. 109-123, (1993)
  • [9] GER R., SEMRL P., The stability of the exponential equation, Proc. Amer. Soc, 124, pp. 779-787, (1996)
  • [10] HYERS D.H., On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A, 27, pp. 222-224, (1941)
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