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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 232630, 9 pages
Ulam Stability of a Quartic Functional Equation
1Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran
2Institute for Mathematical Research, University Putra Malaysia, 43400 UPM, Serdang, Selangor Darul Ehsan, Malaysia
Received 11 January 2012; Revised 9 February 2012; Accepted 13 February 2012
Academic Editor: Nicole Brillouet-Belluot
Copyright © 2012 Abasalt Bodaghi et al. 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.
- J. Baker, “The stability of the cosine equation,” Proceedings of the American Mathematical Society, vol. 80, no. 3, pp. 411–416, 1980.
- S. M. Ulam, Problems in Modern Mathematics, John Wiley & Sons, New York, NY, USA, 1940.
- D. H. Hyers, “On the stability of the linear functional equation,” Proceedings of the National Academy of Sciences of the United States of America, vol. 27, pp. 222–224, 1941.
- T. M. Rassias, “On the stability of the linear mapping in Banach spaces,” Proceedings of the American Mathematical Society, vol. 72, no. 2, pp. 297–300, 1978.
- I. S. Chang, K. W. Jun, and Y. S. Jung, “The modified Hyers-Ulam-Rassias stability of a cubic type functional equation,” Mathematical Inequalities & Applications, vol. 8, no. 4, pp. 675–683, 2005.
- S. Czerwik, “On the stability of the quadratic mapping in normed spaces,” Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, vol. 62, pp. 59–64, 1992.
- M. Eshaghi Gordji and A. Bodaghi, “On the Hyers-Ulam-Rassias stability problem for quadratic functional equations,” East Journal on Approximations, vol. 16, no. 2, pp. 123–130, 2010.
- K. W. Jun and H. M. Kim, “The generalized Hyers-Ulam-Rassias stability of a cubic functional equation,” Journal of Mathematical Analysis and Applications, vol. 274, no. 2, pp. 867–878, 2002.
- J. Lee, J. An, and C. Park, “On the stability of quadratic functional equations,” Abstract and Applied Analysis, vol. 2008, Article ID 628178, 8 pages, 2008.
- S. H. Lee, S. M. Im, and I. S. Hwang, “Quartic functional equations,” Journal of Mathematical Analysis and Applications, vol. 307, no. 2, pp. 387–394, 2005.
- T. Zhou Xu, J. M. Rassias, and W. Xin Xu, “A fixed point approach to the stability of a general mixed additive-cubic functional equation in quasi fuzzy normed spaces,” International Journal of the Physical SciencesInt, vol. 6, no. 2, pp. 313–324, 2011.
- T. Z. Xu, J. M. Rassias, and W. X. Xu, “Generalized Ulam-Hyers stability of a general mixed AQCQ-functional equation in multi-Banach spaces: a fixed point approach,” European Journal of Pure and Applied Mathematics, vol. 3, no. 6, pp. 1032–1047, 2010.
- A. Bodaghi, I. A. Alias, and M. Eshaghi Gordji, “On the stability of quadratic double centralizers and quadratic multipliers: a fixed point approach,” Journal of Inequalities and Applications, vol. 2011, Article ID 957541, 9 pages, 2011.
- A. Bodaghi, I. A. Alias, and M. H. Ghahramani, “Approximately cubic functional equations and cubic multipliers,” Journal of Inequalities and Applications, vol. 2011, 53 pages, 2011.
- J. B. Diaz and B. Margolis, “A fixed point theorem of the alternative, for contractions on a generalized complete metric space,” Bulletin of the American Mathematical Society, vol. 74, pp. 305–309, 1968.
- A. Najati, “On the stability of a quartic functional equation,” Journal of Mathematical Analysis and Applications, vol. 340, no. 1, pp. 569–574, 2008.