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International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 43185, 12 pages
http://dx.doi.org/10.1155/IJMMS/2006/43185

On the stability of generalized d'Alembert and Jensen functional equations

1Department of Mathematics, Kangnam University, Suwon 449-702, South Korea
2School of Computer Science & Mathematics, Victoria University, P.O. Box 14428, Melbourne City 8001, MC, Australia

Received 19 March 2006; Revised 19 July 2006; Accepted 25 July 2006

Copyright © 2006 Hindawi Publishing Corporation. 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. R. Badora, “On Hyers-Ulam stability of Wilson's functional equation,” Aequationes Mathematicae, vol. 60, no. 3, pp. 211–218, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. R. Badora and R. Ger, “On some trigonometric functional inequalities,” in Functional Equations—Results and Advances, vol. 3 of Adv. Math. (Dordr.), pp. 3–15, Kluwer Academic, Dordrecht, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. J. A. Baker, “The stability of the cosine equation,” Proceedings of the American Mathematical Society, vol. 80, no. 3, pp. 411–416, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. A. Baker, J. Lawrence, and F. Zorzitto, “The stability of the equation f(x+y)=f(x)f(y),” Proceedings of the American Mathematical Society, vol. 74, no. 2, pp. 242–246, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. D. G. Bourgin, “Approximately isometric and multiplicative transformations on continuous function rings,” Duke Mathematical Journal, vol. 16, no. 2, pp. 385–397, 1949. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. P. de Place Friis and H. Stetkær, “On the cosine-sine functional equation on groups,” Aequationes Mathematicae, vol. 64, no. 1-2, pp. 145–164, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. P. Găvruţa, “A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings,” Journal of Mathematical Analysis and Applications, vol. 184, no. 3, pp. 431–436, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Pl. Kannappan, “The functional equation f(xy)+f(xy1)=2f(x)f(y) for groups,” Proceedings of the American Mathematical Society, vol. 19, no. 1, pp. 69–74, 1968. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Pl. Kannappan and G. H. Kim, “On the stability of the generalized cosine functional equations,” Annales Academiae Paedagogicae Cracoviensis; Studia Mathematica, vol. 1, pp. 49–58, 2001. View at Google Scholar
  10. G. H. Kim and S. H. Lee, “Stability of the d'Alembert type functional equations,” Nonlinear Functional Analysis & Applications, vol. 9, no. 4, pp. 593–604, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. C. T. Ng, “Jensen's functional equation on groups. III,” Aequationes Mathematicae, vol. 62, no. 1-2, pp. 143–159, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. P. Sinopoulos, “Functional equations on semigroups,” Aequationes Mathematicae, vol. 59, no. 3, pp. 255–261, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. H. Stetkær, “On Jensen's functional equation on groups,” Aequationes Mathematicae, vol. 66, no. 1-2, pp. 100–118, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. L. Székelyhidi, “The stability of d'Alembert-type functional equations,” Acta Scientiarum Mathematicarum (Szeged), vol. 44, no. 3-4, pp. 313–320 (1983), 1982. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. D. Yang, “The stability of Jensen's equation on amenable locally compact groups,” Results in Mathematics, vol. 46, no. 3-4, pp. 381–388, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet