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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 283173, 8 pages
Hyers-Ulam Stability for a Class of Quadratic Functional Equations via a Typical Form
1Department of Mathematics Education, Dankook University, 152 Jukjeon-ro, Suji-gu, Yongin-si, Gyeonggi-do 448-701, Republic of Korea
2Department of Mathematics, Sungshin Women's University, 249-1 Dongseon-dong 3-ga, Seongbuk-gu, Seoul 136-742, Republic of Korea
Received 29 July 2013; Accepted 7 October 2013
Academic Editor: Elena Braverman
Copyright © 2013 Chang Il Kim 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.
- S. M. Ulam, A Collection of Mathematical Problems, Interscience Publisher, New York, NY, USA, 1964.
- 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. Aoki, “On the stability of the linear transformation in Banach spaces,” Journal of the Mathematical Society of Japan, vol. 2, no. 1-2, pp. 64–66, 1950.
- 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.
- 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.
- F. Skof, “Proprieta' locali e approssimazione di operatori,” Rendiconti del Seminario Matematico e Fisico di Milano, vol. 53, no. 1, pp. 113–129, 1983.
- P. W. Cholewa, “Remarks on the stability of functional equations,” Aequationes Mathematicae, vol. 27, no. 1, pp. 76–86, 1984.
- S. Czerwik, “On the stability of the quadratic mapping in normed spaces,” Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, vol. 62, no. 1, pp. 59–64, 1992.
- C. G. Park, “On the stability of the quadratic mapping in Banach modules,” Journal of Mathematical Analysis and Applications, vol. 276, no. 1, pp. 135–144, 2002.
- G. Eskandani, H. Vaezi, and Y. N. Dehghan, “Stability of a mixed additive and quadratic functional equation in non-archimedean banach modules,” Taiwanese Journal of Mathematics, vol. 14, no. 4, pp. 1309–1324, 2010.
- F. Moradlou, H. V. Vaezi, and G. Z. Eskandani, “Hyers-Ulam-Rassias stability of a quadratic and additive functional equation in quasi-Banach spaces,” Mediterranean Journal of Mathematics, vol. 6, no. 2, pp. 233–248, 2009.
- J. M. Rassias, “Solution of the Ulam stability problem for Euler-Lagrange quadratic mappings,” Journal of Mathematical Analysis and Applications, vol. 220, no. 2, pp. 613–639, 1998.
- M. E. Gordji and H. Khodaei, “On the generalized hyers-ulam-rassias stability of quadratic functional equations,” Abstract and Applied Analysis, vol. 2009, Article ID 923476, 11 pages, 2009.
- M. E. Gordji, M. B. Savadkouhi, and C. Park, “Quadratic-quartic functional equations in RN-spaces,” Journal of Inequalities and Applications, vol. 2009, Article ID 868423, 14 pages, 2009.
- K. W. Jun, H. M. Kim, and I. S. Chang, “On the Hyers-Ulam stability of an Euler-Lagrange type cubic functional equation,” Journal of Computational Analysis and Applications, vol. 7, no. 1, pp. 21–33, 2005.
- K. W. Jun, H. M. Kim, and J. Son, “Generalized Hyers-Ulam stability of a quadratic functional equation,” Functional Equations in Mathematical Analysis, vol. 2012, pp. 153–164, 2012.
- K. Ravi, M. Arunkumar, and J. M. Rassias, “Ulam stability for the orthogonally general Euler-Lagrange type functional equation,” International Journal of Mathematics and Statistics, vol. 3, no. 8, pp. 36–46, 2008.
- H. M. Kim, J. M. Rassias, and J. Lee, “Fuzzy approximation of Euler-Lagrange quadratic mappings,” Journal of Inequalities and Applications, vol. 2013, article 358, 15 pages, 2013.