# Duotrigintic functional equation and its stability in Banach spaces

## Main Article Content

## Abstract

In this paper, we introduce a duotrigintic functional equation. Furthermore, we study the Hyers-Ulam stability of a duotrigintic functional equation in Banach spaces by using the direct method.

## Article Details

## References

[1] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950), 64–66. Google Scholar

[2] M. Arunkumar, A. Bodaghi, J. M. Rassias and E. Sathiya, The general solution and approximations of a decic type functional equation in various normed spaces, J. Chungcheong Math. Soc. 29 (2016), 287–328. Google Scholar

[3] A. Bodaghi, Stability of a mixed type additive and quartic function equation, Filomat 28 (2014), 1629–1640. Google Scholar

[4] A. Bodaghi, S. M. Moosavi and H. Rahimi, The generalized cubic functional equation and the stability of cubic Jordan ∗-derivations, Ann. Univ. Ferrara Sez. VII Sci. Mat. 59 (2013), 235–250. Google Scholar

[5] A. Bodaghi, C. Park and J. M. Rassias, Fundamental stabilities of the nonic func- tional equation in intuitionistic fuzzy normed spaces, Commun. Korean Math. Soc. 31 (2016), 729–743. Google Scholar

[6] P. Gaˆvruta, A generalization of the Hyers-Ulam-Rassias stability of approxi- mately additive mappings, J. Math. Anal. Appl. 184 (1994), 431–436. Google Scholar

[7] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. 27 (1941), 222–224. 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), 867–878. Google Scholar

[9] P. Narasimman, Solution and stability of a generalized K-additive functional equation, J. Interdisciplinary Math. 21 (2018), 171–184. Google Scholar

[10] P. Narasimman and R. Amuda, A new method to modelling the additive func- tional equations, Appl. Math. Inf. Sci. 10 (2016), no. 3, 1047–1051. Google Scholar

[11] P. Narasimman and R. Amuda, Stability of an additive functional equation and its application in digital logic circuits, Math. Sci. Lett. 5 (2016), no. 2, 153–159. Google Scholar

[12] M. Nazarianpoor, J. M. Rassias and Gh. Sadeghi, Stability and nonstability of octadecic functional equation in multi-normed spaces, Arabian J. Math. 7 (2018), no. 3, 219–228. Google Scholar

[13] M. Nazarianpoor, J. M. Rassias and Gh. Sadeghi, Solution and stability of quat- tuorvigintic functional equation in intuitionistic fuzzy normed spaces, Iranian J. Fuzzy Syst. 15 (2018), no.4, 13–30. Google Scholar

[14] C. Park, M. Ramdoss, A. R. Aruldass, Stability of trigintic functional equation in multi-Banach spaces: A fixed point approach, Korean J. Math. 26 (2018), 615–628. Google Scholar

[15] M. Ramdoss and A. R. Aruldass, General solution and Hyers-Ulam stability of duotrigintic functional equation in multi-Banach spaces, G. A. Anastassiou and J. M. Rassais (ed.), Frontiers Funct. Equ. Anal. Inequal. Springer, New York, 2019, pp. 125–141. Google Scholar

[16] M. Ramdoss, A. Bodaghi and A. R. Aruldass, General solution and Ulam-Hyers stability of viginti functional equations in multi-Banach spaces, J. Chungcheong Math. Soc. 31, (2018), 199–230. Google Scholar

[17] M. Ramdoss and P. Divyakumari, Modular stability of the generalized quadratic functional equation, J. Emerging Tech. Innov. Research 5 (2018), no. 9, 315–317. Google Scholar

[18] M. Ramdoss and P. Divyakumari, Orthogonal modular stability of radical cubic functional equation, Int. J. Sci. Research Math. Stat. Sci. 6 (2019), no. 1, 237–240. Google Scholar

[19] M. Ramdoss and P. Divyakumari, Stability of radical quartic functional equation, J. Appl. Sci. Comput. 6 (2019), no. 3, 1035–1038. Google Scholar

[20] M. Ramdoss and P. Divyakumari, Orthogonal modular stability of radical quinticf unctional equation, J. Appl. Sci. Comput. 6 (2019), no. 1, 2760–2763. Google Scholar

[21] M. Ramdoss, S. Pinelas and A. R. Aruldass, General solution and a fixed point approach to the Ulam-Hyers stability of viginti duo functional equation in multi-Banach spaces, IOSR J. Math. 13 (2017), no. 4, 48–59. Google Scholar

[22] J. M. Rassias, M. Arunkumar, E. Sathya and T. Namachivayam, Various generalized Ulam-Hyers stabilities of a nonic functional equations, Tbilisi Math. J. 9 (2016), no. 1, 159–196. Google Scholar

[23] J. M. Rassias and M. Eslamian, Fixed points and stability of nonic functional equation in quasi-β-normed spaces, Cont. Anal. Appl. Math. 3, (2015), 293–309. Google Scholar

[24] M. Ramdoss, S. Pinelas and A. R. Aruldass, Ulam-Hyers stability of hexadecic functional equations in multi-Banach spaces, Anal. bf 37 (2017), no. 4, 185–197. Google Scholar

[25] J. M. Rassias, H. Dutta and P. Narasimman, Stability of general A-quartic functional equations in non-Archimedean intuitionistic fuzzy normed spaces, Proc. Jangjeon Math. Soc. 22 2019, 281–290. Google Scholar

[26] J. M. Rassias, M. Ramdoss and A. R. Aruldass, Stability of octavigintic functional equation in multi-Banach spaces: A fixed point approach (preprint). Google Scholar

[27] J. M. Rassias, M. Ramdoss, M. J. Rassias and A. R. Aruldass, General solution, stability and non-stability of quattuorvigintic functional equation in multi-Banach spaces, Int. J. Math. Appl. 5 (2017), 181–194. Google Scholar

[28] J. M. Rassias, M. Ramdoss, M. J. Rassias, V. Vithya and A. R. Aruldass, General solution and stability of quattuorvigintic functional equation in matrix normed Google Scholar

[29] spaces, Tbilisi Math. J. 11 (2018), no. 2, 97–109. Google Scholar

[30] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Am. Math. Soc. 72 (1978), 297–300. Google Scholar