Browse > Article
http://dx.doi.org/10.7858/eamj.2020.004

HYERS-ULAM-RASSIAS STABILITY OF AN ADDITIVE-QUARTIC, A QUADRATIC-QUARTIC, AND A CUBIC-QUARTIC FUNCTIONAL EQUATION  

Jin, Sun-Sook (Department of Mathematics Education, Gongju National University of Education)
Lee, Yang-Hi (Department of Mathematics Education, Gongju National University of Education)
Publication Information
East Asian mathematical journal / v.36, no.1, 2020 , pp. 35-53 More about this Journal
Abstract
In this paper, we investigate Hyers-Ulam-Rassias stability of an additive-quartic functional equation, of a quadratic-quartic functional equation, and of a cubic-quartic functional equation.
Keywords
stability of a functional equation; additive-quartic functional equation; quadratic-quartic functional equation; cubic-quartic functional equation; additive-quartic mappings; quadratic-quartic mappings; cubic-quartic mappings;
Citations & Related Records
연도 인용수 순위
  • Reference
1 S. Abbaszadeh, Intutionistic fuzzy stability of a quadratic and quartic functional equation, Int. J. Nonlinear Anal. Appl. 1 (2010), 100-124.
2 J. Baker, A general functional equation and its stability, Proc. Natl. Acad. Sci. 133(6) (2005), 1657-1664.
3 A. Bodaghi, Stability of a mixed type additive and quartic functional equation, Filomat, 28(8) (2014) 1629-1640.   DOI
4 A. Bodaghi, Approximate mixed type additive and quartic functional equation, Bol. Soc. Paran. Mat. 35(1) (2017), 43-56.   DOI
5 P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431-436.   DOI
6 M. E. Gordji, Stability of a functional equation deriving from quartic and additive functions, arXiv preprint arXiv:0812.5025 (2008).
7 M. E. Gordji, S. Abbaszadeh, and C. Park, On the stability of a generalized quadratic and quartic type functional equation in quasi-Banach spaces, J. Inequal. Appl. 2009 Article ID 153084.
8 M. E. Gordji, A. Ebadian, and S. Zolfaghari, Stability of a functional equation deriving from cubic and quartic functions, Abstr. Appl. Anal. 2008 Article ID 801904.
9 M. E. Gordji, M. B. Savadkouhi, Stability of a mixed type cubic-quartic functional equation in non-archimedean spaces, Appl. Math. Lett. 23 (2010), 1198-1202.   DOI
10 D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222-224.   DOI
11 S.-Y. Jang, C.-K. Park, and D. Y. Shin, Fuzzy stability of a cubic-quartic functional equation: A fixed point approach, Bull. Korean Math. Soc. 48 (2011), 491-503.   DOI
12 H.-M. Kim, On the stability problem for a mixed type of quartic and quadratic functional equation, J. Math. Anal. Appl. 324 (2006), 358-372.   DOI
13 J.-R. Lee, C.-K. Park, Y.-J. Cho and D.-Y. Shin, Orthogonal stability of a cubic-quartic functional equation in non-archimedean spaces, J. Comput. Anal. Appl. 15 (2013), 572-583.
14 C.-K. Park, Orthogonal stability of a cubic-quartic functional equation, Journal of Nonlinear Sciences & Applications (JNSA) 5 (2012), 28-36.   DOI
15 Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.   DOI
16 S. M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1960.
17 Z. Wang and P. K. Sahoo, Stability of the generalized quadratic and quartic type functional equation in non-archimedean fuzzy normed spaces, J. Appl. Anal. Comput. 6 (2016), 917-938.
18 M. E. Gordji, M. B. Savadkouhi, and C. Park, Quadratic-quartic functional equations in RN-spaces, J. Inequal. Appl. 2009 Article ID 868423.
19 T. Z. Xu, J. M. Rassias, and W. X. Xu, A generalized mixed quadratic-quartic functional equation, Bull. Malays. Math. Sci. Soc. 35(3) (2012), 633-649.
20 X. Zhao, X. Yang, and C. T. Pang, Solution and stability of a general mixed type cubic and quartic functional equation, J. Funct. Spaces Appl. 2013 Article ID 673810.