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On a composite functional equation related to the Golab-Schinzel equation

Themistocles M. Rassias|Madjid Eshaghi Gordji|Mohamed Tial|Driss Zeglami
대한수학회 (The Korean Mathematical Society)|2016.03|대한수학회보 (Bulletin of the KMS)|제53권 제2호|pp. 387-398

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참고문헌

키워드

Hyers-Ulam stabilitysuperstabilityGolab--Schinzel equation
주제분류수학

초록

Let $X$ be a vector space over a field $K$ of real or complex numbers and $ k\in \mathbb{N}$. We prove the superstability of the following generalized Golab--Schinzel type equation \begin{equation*} f(x_{1}+\sum_{i=2}^{p}x_{i}f(x_{1})^{k} f(x_{2})^{k}\cdots f(x_{i-1})^{k})=\prod \limits_{i=1}^{p}f(x_{i}),\ x_{1},x_{2},\ldots,x_{p}\in X, \end{equation*} where $f:X\rightarrow K$ is an unknown function which is hemicontinuous at the origin.

Abstract

Let $X$ be a vector space over a field $K$ of real or complex numbers and $ k\in \mathbb{N}$. We prove the superstability of the following generalized Golab--Schinzel type equation \begin{equation*} f(x_{1}+\sum_{i=2}^{p}x_{i}f(x_{1})^{k} f(x_{2})^{k}\cdots f(x_{i-1})^{k})=\prod \limits_{i=1}^{p}f(x_{i}),\ x_{1},x_{2},\ldots,x_{p}\in X, \end{equation*} where $f:X\rightarrow K$ is an unknown function which is hemicontinuous at the origin.

참고문헌 (34)

  1. J. Aczel, "Remarks on one-parameter subsemigroups of the affine group and their homo- and isomorphisms", Aequationes Math, 4, pp.1~10 (1970)
  2. J. A. Baker, "The stability of the cosine equation", Proc. Amer. Math. Soc, 80(3), pp.411~416 (1980)
  3. J. A. Baker, "The stability of the equation f(x + y) =f(x)f(y)", Proc. Amer. Math. Soc, 74(2), pp.242~246 (1979)
  4. K. Baron, "On the continuous solutions of the Golab–Schinzel equation", Aequationes Math, 38(2-3), pp.155~162 (1989)
  5. N. Brillouet-Belluot, "On some functional equations of Golab–Schinzel type", Aequationes Math, 42(2-3), pp.239~270 (1991)
  6. N. Brillouet-Belluot, "On some recent developments in Ulam’s type stability", Abstr. Appl. Anal, 2012, pp.41~ (2012)
  7. N. Brillouet-Belluot, "Equations fonctionnelles et recherche de sous-groupes", Aequationes Math, 31(2-3), pp.253~293 (1986)
  8. J. Brzdek, "Subgroups of the group Zn and a generalization of the Golab–Schinzel func-tional equation", Aequationes Math, 43(1), pp.59~71 (1992)
  9. J. Brzdek, "Some remarks on solutions of the functional equation f(x + f(x)ny) =tf(x)f(y)", Publ. Math. Debrecen, 43(1-2), pp.147~160 (1993)
  10. J. Brzdek, "Golab–Schinzel equation and its generalizations", Aequationes Math, 70(1-2), pp.14~24 (2005)
  11. J. Brzdek, "Stability of the generalized Golab–Schinzel equation", Acta Math. Hungar, 113, pp.115~126 (2006)
  12. J. Brzdek, "On the quotient stability of a family of functional equations", Nonlinear Anal, 71(10), pp.4396~4404 (2009)
  13. J. Brzdek, "On stability of a family of functional equations", Acta Math. Hungar, 128(1-2), pp.139~149 (2010)
  14. J. Brzdek, "Hyperstability and superstability", Abstr. Appl. Anal, 2013, pp.13~ (2013)
  15. A. Chahbi, "On the superstability of the generalized Golab–Schinzel equation", Internat. J. Math. Anal, 6(54), pp.2677~2682 (2012)
  16. A. Charifi, "On the stability of Pexiderized Golab-Schinzel equation", Comput. Math. Appl, 59(9), pp.3193~3202 (2010)
  17. J. Chudziak, "Approximate solutions of the Golab–Schinzel equation", J. Approx. Theory, 136(1), pp.21~25 (2005)
  18. J. Chudziak, "Stability of the generalized Golab–Schinzel equation", Acta Math. Hungar, 113(1-2), pp.133~144 (2006)
  19. J. Chudziak, "Approximate solutions of the generalized Golab–Schinzel equation", J. Inequal. Appl, 2006, pp.8~ (2006)
  20. J. Chudziak, "Stability problem for the Golab–Schinzel type functional equations", J. Math. Anal. Appl, 339(1), pp.454~460 (2008)
  21. J. Chudziak, "On the stability of the Golab–Schinzel functional equation", J. Math. Anal. Appl, 302(1), pp.196~200 (2005)
  22. R. Ger, "The stability of the exponential equation", Proc. Amer. Math. Soc, 124(3), pp.779~787 (1996)
  23. S. Golab, "Sur l’equation fonctionnelle f(x + yf(x)) = f(x)f(y)", Publ. Math. Debrecen, 6, pp.113~125 (1959)
  24. D. H. Hyers, "Stability of Functional Equations in Sev-eral Variables", Progress in Nonlinear Differential Equations and their Applications, pp.34~ (1998), Birkhauser
  25. E. Jablonska, "Functional Equations in Mathematical Analysis", pp.509~521 (2012), Springer
  26. E. Jablonska, "On continuous solutions of an equation of the Golab–Schinzel type", Bull. Aust. Math. Soc, 87(1), pp.10~17 (2013)
  27. E. Jablonska, "On locally bounded above solutions of an equation of the Golab–Schinzel type", Aequationes Math, 87(1-2), pp.125~133 (2014)
  28. S. M. Jung, "Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Anal-ysis" (2011), Springer
  29. Th. M. Rassias, "On the stability of linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72, pp.297~300 (1978)
  30. A. Roukbi, "Hyers-Ulam stability of Wilson’s functional equation", Math. Sci. Adv. Appl, 22, pp.19~26 (2013)
  31. D. Zeglami, "The superstability of a variant of Wilson’s functional equations on an ar-bitrary group", Afr. Mat, 26, pp.609~617 (2015)
  32. D. Zeglami, "On the supesrtability of trigonometric type functional equa-tions", British J. Math. & Comput. Sci, 4(8), pp.1146~1155 (2014)
  33. D. Zeglami, "Functional Equations inMathematical Analysis", pp.337~358 (2012), Springer
  34. D. Zeglami, "Hyers-Ulam stability of generalized Wilson’s and d’Alembert’s functional equations", Afr. Mat, 26, pp.215~223 (2015)

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