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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 454569, 7 pages
http://dx.doi.org/10.1155/2014/454569
Research Article

Hyers-Ulam Stability of Iterative Equation in the Class of Lipschitz Functions

Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China

Received 14 March 2014; Revised 10 May 2014; Accepted 10 May 2014; Published 1 June 2014

Academic Editor: Krzysztof Ciepliński

Copyright © 2014 Chao Xia and Wei Song. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. N. Brillouët-Belluot, J. Brzdęk, and K. Ciepliński, “On some recent developments in Ulam's type stability,” Abstract and Applied Analysis, Article ID 716936, 41 pages, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, vol. 48 of Springer Optimization and Its Applications, Springer, New York, NY, USA, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  3. R. P. Agarwal, B. Xu, and W. Zhang, “Stability of functional equations in single variable,” Journal of Mathematical Analysis and Applications, vol. 288, no. 2, pp. 852–869, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. M. Kuczma, B. Choczewski, and R. Ger, Iterative Functional Equations, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  5. K. Baron and W. Jarczyk, “Recent results on functional equations in a single variable, perspectives and open problems,” Aequationes Mathematicae, vol. 61, no. 1-2, pp. 1–48, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. C. Nabeya, “On the functional equation f(p+qx+rf(x))=a+bx+cf(x),” Aequationes Mathematicae, vol. 11, no. 2-3, pp. 199–211, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. Z. Zhang, L. Yang, and W. N. Zhang, Iterative Equations and Embedding Flow, Shanghai Scientific and Technological Education, 1998.
  8. W. N. Zhang, K. Nikodem, and B. Xu, “Convex solutions of polynomial-like iterative equations,” Journal of Mathematical Analysis and Applications, vol. 315, no. 1, pp. 29–40, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. B. Xu and W. Zhang, “Decreasing solutions and convex solutions of the polynomial-like iterative equation,” Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 483–497, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. W. N. Zhang, “On the differentiable solutions of the iterated equation i=1nλifi(x)=F(x),” Chinese Science Bulletin, vol. 32, no. 21, pp. 1444–1451, 1987. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. M. Kulczycki and J. Tabor, “Iterative functional equations in the class of Lipschitz functions,” Aequationes Mathematicae, vol. 64, no. 1-2, pp. 24–33, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. V. Murugan and P. V. Subrahmanyam, “Existence of solutions for equations involving iterated functional series,” Fixed Point Theory and Applications, vol. 2005, no. 2, pp. 219–232, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. V. Murugan and P. V. Subrahmanyam, “Special solutions of a general iterative functional equation,” Aequationes Mathematicae, vol. 72, no. 3, pp. 269–287, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. V. Murugan and P. V. Subrahmanyam, “Special solutions of a general iterative functional equation,” Aequationes Mathematicae, vol. 72, no. 3, pp. 269–287, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. V. Murugan and P. V. Subrahmanyam, “Special solutions of a general iterative functional equation,” Aequationes Mathematicae, vol. 76, no. 3, pp. 317–320, 2008. View at Google Scholar
  16. D. L. Yang and W. N. Zhang, “Characteristic solutions of polynomial-like iterative equations,” Aequationes Mathematicae, vol. 67, no. 1-2, pp. 80–105, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. B. Xu and W. N. Zhang, “Hyers-Ulam stability for a nonlinear iterative equation,” Colloquium Mathematicum, vol. 93, no. 1, pp. 1–9, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet