×

zbMATH — the first resource for mathematics

A general uniqueness theorem concerning the stability of AQCQ type functional equations. (English) Zbl 1433.39011
Summary: In this paper, we prove a general uniqueness theorem which is useful for proving the uniqueness of the relevant additive mapping, quadratic mapping, cubic mapping, quartic mapping, or the additive-quadratic-cubic-quartic mapping when we investigate the (generalized) Hyers-Ulam stability.
MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] S. Abbaszadeh,Intuitionistic fuzzy stability of a quadraric and quartic functional equation, Int. J. Nonlinear Anal. Appl.,1(2010), 100-124. · Zbl 1281.39033
[2] M. Eshaghi and H. Khodaei,Solution and stability of generalized mixed type cubic, quadratic and additive functional equation in quasi-Banach spaces, Nonlinear Anal., 71(2009), 5629-5643. · Zbl 1179.39034
[3] P. G˘avruta,A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl.,184(1994), 431-436. · Zbl 0818.46043
[4] D. H. Hyers,On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA,27(1941), 222-224. · Zbl 0061.26403
[5] S. S. Jin and Y. H. Lee,Fuzzy stability of the Cauchy additive and quadratic type functional equation, Commun. Korean Math. Soc.,27(2012), 523-535. · Zbl 1251.39024
[6] S.-M. Jung, D. Popa and M. Th. Rassias,On the stability of the linear functional equation in a single variable on complete metric groups, J. Global Optim.,59(1)(2014), 165-171. · Zbl 1295.33004
[7] H. Khodaei,On the stability of additive, quadratic, cubic and quartic set-valued functional equations, Results Math.,68(2015), 1-10. · Zbl 1330.39029
[8] Y.-H. Lee and S.-M. Jung,A general uniqueness theorem concerning the stability of additive and quadratic functional equations, J. Funct. Spaces, (2015), Article ID 643969, 8 pp.
[9] Y.-H. Lee and S.-M. Jung,A general uniqueness theorem concerning the stability of monomial functional equations in fuzzy spaces, J. Inequal. Appl., (2015), 2015:66, 11 pp.
[10] Y.-H. Lee and S.-M. Jung,General uniqueness theorem concerning the stability of additive, quadratic, and cubic functional equations, Adv. Difference Equ., (2016), Paper No. 75, 12 pp.
[11] Y.-H. Lee, S.-M. Jung and M. Th. Rassias,Uniqueness theorems on functional inequalities concerning cubic-quadratic-additive equation, J. Math. Inequal.,12(1)(2018), 43-61. · Zbl 1412.39028
[12] A. Najati and M. B. Moghimi,Stability of a functional equation deriving from quadratic and additive functions in quasi-Banach spaces, J. Math. Anal. Appl., 337(2008), 399-415. · Zbl 1127.39055
[13] P. Nakmahachalasint,On the generalized Ulam-Gavruta-Rassias stability of mixedtype linear and Euler-Lagrange-Rassias functional equations, Int. J. Math. Math. Sci., (2007), Article ID 63239, 10 pp. · Zbl 1148.39026
[14] S. Ostadbashi and J. Kazemzadeh,Orthogonal stability of mixed type additive and cubic functional equations, Int. J. Nonlinear Anal. Appl.,6(2015), 35-43.
[15] C. Park, M. E. Gordji, M. Ghanifard and H. Khodaei,Intuitionistic random almost additive-quadratic mappings, Adv. Difference Equ., (2012), 2012:152, 15 pages. · Zbl 1377.39043
[16] Th. M. Rassias,On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc.,72(1978), 297-300. · Zbl 0398.47040
[17] W. Towanlong and P. Nakmahachalasint,Ann-dimensional mixed-type additive and quadratic functional equation and its stability, ScienceAsia,35(2009), 381-385.
[18] S. M. Ulam,
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.