多元二次函数方程在限制定义域上的稳定性
The Stability of a Multi-Quadratic Functional Equation on a Restricted Domain
DOI: 10.12677/ORF.2016.64014, PDF, HTML, XML, 下载: 1,669  浏览: 5,246  科研立项经费支持
作者: 王 琳：青岛科技大学数理学院，山东 青岛；纪培胜, 刘韦韦：青岛大学数学与统计学院，山东 青岛
关键词: Hyers-Ulam稳定性；函数方程；多元二次函数方程；Hyers-Ulam Stability； Functional Equation； Multi-Quadratic Functional Equation
摘要: 本文证明了多元二次函数方程在限制定义域上的稳定性。
Abstract: In this paper, we obtain the stability of the multi-quadratic functional equation on a restricted domain.
文章引用：王琳, 纪培胜, 刘韦韦. 多元二次函数方程在限制定义域上的稳定性[J]. 运筹与模糊学, 2016, 6(4): 107-114. http://dx.doi.org/10.12677/ORF.2016.64014

参考文献

[1] Ulam, S.M. (1960) A Collection of Mathematical Problems. Interscience, New York.
[2] Hyers, D.H. (1941) On the Stability of the Linear Functional Equation. Proceedings of the National Academy of Sciences of the United States of America, 27, 222-224.
http://dx.doi.org/10.1073/pnas.27.4.222
[3] Kominek, Z. (1989) On a Local Stability of the Jensen Functional Equation. De-monstratio Mathematica, 22, 499-507.
[4] Jung, S.M. (1998) Hyers-Ulam-Rassias Stability of Jensen’s Equation and Its Applica-tion. Proceedings of the American Mathematical Society, 126, 3137-3143.
http://dx.doi.org/10.1090/S0002-9939-98-04680-2
[5] Rassias, J.M. (2002) On the Ulam Stability of Mixed Type Mappings on Restricted Domains. Journal of Mathematical Analysis and Applications, 276, 747-762.
http://dx.doi.org/10.1016/S0022-247X(02)00439-0
[6] Hyers, D.H., Isac, G. and Rassias, Th.M. (1998) On the Asymptoticity Aspect of Hyers-Ulam Stability of Mappings. Proceedings of the American Mathematical Society, 126, 425-430.
http://dx.doi.org/10.1090/S0002-9939-98-04060-X
[7] Wolna, D. (2006) The Stability of Monomial Functions on a Restricted Domain. Aequationes Mathematicae, 72, 100- 109.
http://dx.doi.org/10.1007/s00010-006-2832-z
[8] Rassias, J.M. and Rassias, M.J. (2003) On the Ulam Stability of Jensen and Jensen Type Mappings on Restricted Domains. Journal of Mathematical Analysis and Applications, 281, 516-524.
http://dx.doi.org/10.1016/S0022-247X(03)00136-7
[9] Chung, J.Y., Kim, D. and Rassias, J.M. (2012) Stability of Jensen Type Functional Equations on Restricted Domains in a Group and Their Asymptotic Behaviors. Journal of Applied Mathematics, 2012, 1-12.
http://dx.doi.org/10.1155/2012/691981
[10] Lee, Y.-H. (2013) Hyers-Ulam-Rassias Stability of a Quadratic Additive Type Functional Equation on a Restricted Domain. International Journal of Mathematical Analysis, 7, 2745-2752.
http://dx.doi.org/10.12988/ijma.2013.39224
[11] Parka, W.-G. and Baeb, J.-H. (2005) On a Bi-Quadratic Functional Equation and Its Stability. Nonlinear Analysis, 62,643-654.
http://dx.doi.org/10.1016/j.na.2005.03.075
[12] Ji, P.S., Qi, W.Q. and Zhan, X.J. (2014) Generalized Stability of Multi-Quadratic Mappings. Journal of Mathematics Research with Applications, 34, 209-215.

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