Korean J. Math. Vol. 30 No. 2 (2022) pp.403-412
DOI: https://doi.org/10.11568/kjm.2022.30.2.403

General solution and Ulam stability of generalized CQ functional equation

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Published: Jun 30, 2022
Keywords:
Ulam stability, non-Archimedean space, cubic functional equation, quartic functional
Mathematics Subject Classification:
39B22, 39B82, 46S10

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Vediyappan Govindan
Department of Mathematics, DMI St John Baptist University, Mangochi, Malawi
Jung-Rye Lee
Department of Data Science, Daejin University, Kyunggi 11159, Korea
Sandra Pinelas
Departamento de Cieˆncias Exatas e Engenharia, Academia Militar, Portugal
P. Muniyappan
Erode Arts and Science College (Autonomous), Erode, Tamil Nadu, India

Abstract

In this paper, we introduce the following cubic-quartic functional equation of the form
$$ f(x+4y)+f(x-4y)=16\left[f(x+y)+f(x-y)\right]\pm 30f(-x)+\frac{5}{2}\left[f(4y)-64f(y)\right]. $$
Further, we investigate the general solution and the Ulam stability for the above functional equation in non-Archimedean spaces by using the direct method.



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References

[1] M. Eshaghi Gordji, R. Khodabakhsh, S. Jung and H. Khodaei, AQCQ-Functional equation in nonArchimedean normed spaces, Abs. Appl. Anal. 2010 (2010), Article ID 741942. Google Scholar

[2] M. Eshaghi Gordji, H. Khodaei and R. Khodabakhsh, General quartic-cubic-quadratic functional equation Google Scholar

[3] in non-Archimedean normed spaces, UPB Sci. Bull. Ser. A, 72 (2010), no. 3, 69-84. Google Scholar

[4] M. Eshaghi Gorgji and M. B. Savadkouhi, Stability of cubic and quartic functional equations in non-Archimedean spaces, Acta Appl. Math. 110 (2010), 1321-1329. Google Scholar

[5] M. Eshaghi Gordji and M. B. Savadkouhi, Stability of a mixed type cubic-quartic functional equation in non-Archimedean spaces, Appl. Math. Lett. 23 (2010), 1198-1202. Google Scholar

[6] A. Gil'anyi, On a problem by K. Nikodem, Math. Inequal. Appl. 5 (2002), 707-710. Google Scholar

[7] V. Govindan, S. Murthy and M. Saravanan, Solution and stability of new type of (aaq,bbq,caq,daq) mixed type functional equation in various normed spaces: Using two different methods, Int. J. Math. Appl. 5 (2017), 187-211. Google Scholar

[8] K. Jun and H. Kim, The generalized Hyers-Ulam-Rassias stability of a cubic functional equation, J. Math. Anal. Appl. 274 (2002), 267-278. Google Scholar

[9] S. Jung, D. Popa and M. Th. Rassias, On the stability of the linear functional equation in a single variable on complete metric spaces, J. Global Optim. 59 (2014), 13-16. Google Scholar

[10] Y. Lee, S. Jung and M. Th. Rassias, Uniqueness theorems on functional inequalities concerning cubic-quadratic-additive equation, J. Math. Inequal. 12 (2018), 43-61. Google Scholar

[11] D. Mihet, The stability of the additive Cauchy functional equation in non- Archimedean fuzzy normed spaces, Fuzzy Sets Syst. 161 (2010), 2206-2212. Google Scholar

[12] R. Murali, S. Pinelas and V. Vithya, The stability of viginti unus functional equation in various spaces, Global J. Pure Appl. Math. 13 (2017), 5735-5759. Google Scholar

[13] S. Murthy, V. Govindhan, General solution and generalized HU (Hyers-Ulam) statbility of new dimension cubic functional equation in fuzzy ternary Banach algebras: Using two different methods, Int. J. Pure Appl. Math. 113 (2017), no. 6, 394-403. Google Scholar

[14] P. Narasimman, K. Ravi and S. Pinelas, Stability of Pythagorean mean functional equation, Global J. Math. 4 (2015), 398-411. Google Scholar

[15] C. Park, Additive -functional inequalities and equations, J. Math. Inequal. 9 (2015), 17-26. Google Scholar

[16] C. Park, Additive -functional inequalities in non-Archimedean normed spaces, J. Math. Inequal. 9 (2015), 397-407. Google Scholar

[17] S. Pinelas, V. Govindan and K. Tamilvanan, Stability of non-additive functional equation, IOSR J. Math. 14 (2018), no. 2, 70-78. Google Scholar