Abstract
We prove the generalized stability of
Research Article | Open AccessGeneralized Stability of
Generalized Stability of C *
Academic Editor: Bruce D. Calvert
Received10 Sept 2006
Revised22 Jan 2007
Accepted15 Feb 2007
Published22 Mar 2007
References
H. Zettl, “A characterization of ternary rings of operators,” Advances in Mathematics, vol. 48, no. 2, pp. 117–143, 1983.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. S. Moslehian, “Almost derivations on -ternary rings,” Bulletin of the Belgian Mathematical Society Simon Stevin, vol. 14, pp. 135–142, 2007.
View at: Google ScholarS. M. Ulam, A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, no. 8, Interscience Publishers, New York, NY, USA, 1960.
View at: Zentralblatt MATH | MathSciNetD. 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, no. 4, pp. 222–224, 1941.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetTh. 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.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetP. 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 Site | Google Scholar | Zentralblatt MATH | MathSciNetC. Park, “Isomorphisms between -ternary algebras,” Journal of Mathematical Physics, vol. 47, no. 10, Article ID 103512, 12 pages, 2006.
View at: Publisher Site | Google Scholar | MathSciNetC. Park, “Isomorphisms between -ternary algebras,” Journal of Mathematical Analysis and Applications, vol. 327, no. 1, pp. 101–115, 2007.
View at: Publisher Site | Google Scholar | MathSciNetF. Skof, “Proprietà locali e approssimazione di operatori,” Rendiconti del Seminario Matematico e Fisico di Milano, vol. 53, pp. 113–129, 1983.
View at: Google Scholar | Zentralblatt MATH | MathSciNetP. W. Cholewa, “Remarks on the stability of functional equations,” Aequationes Mathematicae, vol. 27, no. 1, pp. 76–86, 1984.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetSt. 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.
View at: Google Scholar | Zentralblatt MATH | MathSciNetC. 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.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetK.-W. Jun and Y.-H. Lee, “On the Hyers-Ulam-Rassias stability of a Pexiderized quadratic inequality,” Mathematical Inequalities & Applications, vol. 4, no. 1, pp. 93–118, 2001.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. Mirzavaziri and M. S. Moslehian, “A fixed point approach to stability of a quadratic equation,” Bulletin of the Brazilian Mathematical Society. New Series, vol. 37, no. 3, pp. 361–376, 2006.
View at: Publisher Site | Google Scholar | MathSciNet
Copyright
Copyright © 2007 Choonkil Park and Jianlian Cui. 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.