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http://dx.doi.org/10.14403/jcms.2021.34.3.295

ON THE STABILITY OF THE GENERAL SEXTIC FUNCTIONAL EQUATION  

Chang, Ick-Soon (Department of Mathematics Chungnam National University)
Lee, Yang-Hi (Department of Mathematics Education Gongju National University of Education)
Roh, Jaiok (Ilsong College of Liberal Arts Hallym University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.34, no.3, 2021 , pp. 295-306 More about this Journal
Abstract
The general sextic functional equation is a generalization of many functional equations such as the additive functional equation, the quadratic functional equation, the cubic functional equation, the quartic functional equation and the quintic functional equation. In this paper, motivating the method of Găvruta [J. Math. Anal. Appl., 184 (1994), 431-436], we will investigate the stability of the general sextic functional equation.
Keywords
sextic functional equations; stability; Hyers-Ulam stability;
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1 D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA, 27 (1941), 222-224.   DOI
2 G. Isac and T. M. Rassias, On the Hyers-Ulam stability of ψ-additive mappings, J. Approx. Theory, 72 (1993), 131-137.   DOI
3 K.-W. Jun and H.-M. Kim, On the Hyers-Ulam-Rassias stability of a general cubic functional equation, Math. Inequal. Appl., 6 (2003), 289-302.
4 Y.-H. Lee, Stability of a monomial functional equation on a restricted domain, Mathematics, 5 (2017), 53.   DOI
5 Y.-H. Lee, On the Hyers-Ulam-Rassias stability of a general quartic functional equation, East Asian Math. J., 35 (2019), no. 3, 351-356.   DOI
6 S. Alshybani, S. M. Vaezpour and R. Saadati, Generalized Hyers-Ulam stability of sextic functional equation in random normed spaces, J. Comput. Anal. Appl., 24 (2018), no. 2, 370-381.
7 S. Alshybani, S. M. Vaezpour and R. Saadati, Stability of the sextic functional equation in various spaces, J. Inequal. Spec. Funct., 9 (2018), no. 4, 8-27.
8 J. Baker, A general functional equation and its stability, Proc. Natl. Acad. Sci., 133 (2005), no. 6, 1657-1664.
9 Y. J. Cho, M. B. Ghaemi, M. Choubin and M. E. Gordji, On the Hyers-Ulam stability of sextic functional equations in β-homogeneous probabilistic modular spaces, Math. Inequal. Appl., 16 (2013), no. 4, 1097-1114.
10 I. I. EL-Fassi, New stability results for the radical sextic functional equation related to quadratic mappings in (2, β)-Banach spaces, J. Fixed Point Theory Appl., 20 (2018), 138, 1-17.   DOI
11 Z. Gajda, On stability of additive mappings, Int. J. Math. Math. Sci., 14 (1991), no. 3, 431-434.   DOI
12 Y.-H. Lee, On the Hyers-Ulam-Rassias stability of the generalized polynomial function of degree 2, J. Chungcheong Math. Soc., 22 (2009), no.2, 201-209.
13 P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436.   DOI
14 S.-M. Jung, On the Hyers-Ulam-Rassias stability of approximately additive map-pings, J . Math. Anal. Appl., 204 (1996), 221-226.   DOI
15 Y.-H. Lee, On the generalized Hyers-Ulam stability of the generalized polynomial function of degree 3, Tamsui Oxf. J. Math. Sci,. 24 (2008), no. 4, 429-444.
16 A. Najati and C. Park, Fixed Points and Stability of a Generalized Quadratic Functional Equation J. Inequal. Appl., 2009(2009), Article ID 193035, 19 pages.
17 T. Xu, J. Rassias, M. Rassias and W. Xu, Stability of quintic and sextic functional equations in non-archimedean fuzzy normed spaces, Eighth International Conference on Fuzzy Systems and Knowledge Discovery, 2011.
18 S.M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1960.
19 J. Roh, Y. H. Lee and S. -M. Jung The Stability of a General Sextic Functional Equation by Fixed Point Theory, J. Funct. Spaces, 2020 (2020), 1-8.   DOI
20 Y.-H. Lee and K. W. Jun, On the stability of approximately additive mappings, Proc. Amer. Math. Soc., (2000), 1361-1369.
21 Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300.   DOI
22 T. Xu, J. Rassias, M. Rassias and W. Xu, A fixed point approach to the stability of quintic and sextic functional equations in quasi-β-normed spaces, J. Inequal. Appl., 2010 (2010), Article ID 423231, 23 pages.
23 K. Ravi and S. Sabarinathan, Generalized Hyers-Ulam stability of a sextic functional equation in paranormed spaces, International Journal of Mathematics Trends and Technology, 9 (2014), no. 1, 61-69.   DOI
24 S. Ostadbashi and M. Soleimaninia, On the stability of the orthogonal pexiderized quartic functional equations, Nonlinear Funct. Anal. Appl., 20 (2015), no. 4, 539-549.
25 Y.-H. Lee, On the Hyers-Ulam-Rassias stability of a general quintic functional equation and a general sextic functional equation, Mathematics, 7 (2019), 510.   DOI