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http://dx.doi.org/10.5666/KMJ.2018.58.2.291

A General Uniqueness Theorem concerning the Stability of AQCQ Type Functional Equations  

Lee, Yang-Hi (Department of Mathematics Education, Gongju National University of Education)
Jung, Soon-Mo (Mathematics Section, College of Science and Technology, Hongik University)
Publication Information
Kyungpook Mathematical Journal / v.58, no.2, 2018 , pp. 291-305 More about this Journal
Abstract
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.
Keywords
uniqueness; stability; Hyers-Ulam stability; generalized Hyers-Ulam stability; AQCQ type functional equation; AQCQ mapping;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 S. Abbaszadeh, Intuitionistic fuzzy stability of a quadraric and quartic functional equation, Int. J. Nonlinear Anal. Appl., 1(2010), 100-124.
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.   DOI
3 P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184(1994), 431-436.   DOI
4 D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA, 27(1941), 222-224.   DOI
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.   DOI
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.   DOI
7 H. Khodaei, On the stability of additive, quadratic, cubic and quartic set-valued functional equations, Results Math., 68(2015), 1-10.   DOI
8 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.
9 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.
10 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, 11pp.   DOI
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.
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.   DOI
13 P. Nakmahachalasint, On the generalized Ulam-Gavruta-Rassias stability of mixed-type linear and Euler-Lagrange-Rassias functional equations, Int. J. Math. Math. Sci., (2007), Article ID 63239, 10 pp.
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 S. M. Ulam, A collection of mathematical problems, Interscience Publ., New York, 1960.
16 C. Park, M. E. Gordji, M. Ghanifard and H. Khodaei, Intuitionistic random almost additive-quadratic mappings, Adv. Difference Equ., (2012), 2012:152, 15 pages.
17 Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72(1978), 297-300.   DOI
18 W. Towanlong and P. Nakmahachalasint, An n-dimensional mixed-type additive and quadratic functional equation and its stability, ScienceAsia, 35(2009), 381-385.   DOI