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Hyers-Ulam stability of a quadratic-additive functional equation in non-Archimedean fuzzy $\varphi$-2-normed spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 1، دوره 16، شماره 4، تیر 2025، صفحه 1-13 اصل مقاله (457.52 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.28228.3838 | ||
| نویسندگان | ||
| Kandhasamy Tamilvanan1؛ Jung Rye Lee* 2؛ Choonkil Park3 | ||
| 1Department of Mathematics, Government Arts College for Men, Krishnagiri- 635 001, Tamil Nadu, India | ||
| 2Department of Data Science, Daejin University, Kyunggi 11159, Korea | ||
| 3Research Institute for Convergence of Basic Science, Hanyang University, Seoul 04763, Korea | ||
| تاریخ دریافت: 10 مرداد 1401، تاریخ پذیرش: 11 شهریور 1401 | ||
| چکیده | ||
| In this work, we introduce the following quadratic-additive functional equation \begin{align*} &\psi\left(\sum_{a=1}^{n} v_{a}\right)+\sum_{a=1}^{n}\psi\left(-v_{a}+\sum_{b=1;a\neq b}^{n} v_{b}\right)\nonumber \\= &\left(n-3\right) \sum_{1\leq a<b\leq n}\psi\left( v_{a}+ v_{b}\right)-\left(n^{2}-5n+2\right)\sum_{a=1}^{n} \left[ \frac{\psi(v_{a})+\phi(-v_{a})}{2}\right] -\left(n^{2}-5n+4\right)\sum_{a=1}^{n} \left[\frac{\psi(v_{a})-\phi(-v_{a})}{2}\right] \end{align*} where $n$ is a nonnegative integer in $\mathbb{N}-\{0,1,2\}$, and we prove the Hyers-Ulam stability of the quadratic-additive functional equation in non-Archimedean fuzzy $\varphi$-2-normed space by utilizing two different techniques. | ||
| کلیدواژه‌ها | ||
| Hyers-Ulam stability؛ non-Archimedean $\varphi$-2-normed space؛ quadratic-additive functional equation؛ fixed point method | ||
| مراجع | ||
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[1] M. Almahalebi, S. Kabbaj, and G. Kim, On the hyperstability of Jensen functional equation in 2-Banach spaces, Fixed Point Theory 20 (2019), 417–429. [2] A. Bodaghi and B. Shojaee, On an equation characterizing multi-cubic mappings and its stability and hyperstability, Fixed Point Theory 22 (2021), 83–92. [3] L. C˘adariu and V. Radu, Fixed points and the stability of Jensen’s functional equation, J. Inequal. Pure Appl. Math. 4 (2003), no. 1, Paper No. 4. [4] J. Diaz and B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Am. Math. Soc. 74 (1968), 305–309. [5] I. El-Fassi, E. Elqorachi, and H. Khodaei, A fixed point approach to stability of k-th radical functional equation in non-Archimedean (n, β)-Banach spaces, Bull. Iran. Math. Soc. 47 (2021), 487–504. [6] M. Eshaghi Gordji, H. Khodaei, and M. Kamyar, Stability of Cauchy-Jensen type functional equation in generalized fuzzy normed spaces, Comput. Math. Appl. 62 (2011), 2950–2960. [7] M. Eshaghi Gordji and M.B. Savadkouhi, Stability of cubic and quartic functional equations in non-Archimedean spaces, Acta Appl. Math. 110 (2010), 1321–1329. [8] 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. [9] Z. Gajda, On stability of additive mappings, Int. J. Math. Math. Sci. 14 (1991), no. 3, 431–434. [10] K. Hensel, Uber eine neue Begru¨ndung der Theorie der algebraischen Zahlen, Jahresbericht Deutschen Math.-Verein. 6 (1897), 83–88. [11] D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941), 222–224. [12] 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. [13] Y. Lee, S. Jung, M. Th. Rassias, Uniqueness theorems on functional inequalities concerning cubic-quadratic-additive equation, J. Math. Inequal. 12 (2018), 43–61. [14] H. Khodaei and Th.M. Rassias, Set-valued dynamics related to generalized Euler-Lagrange functional equations, J. Fixed Point Theory Appl. 20 (2018), Paper No. 32. [15] A. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Kluwer Academic Publishers, Dordrecht, 1997. [16] S.A. Mohiuddine and M.A. Alghamdi, Stability of functional equation obtained through a fixed-point alternative in intuitionistic fuzzy normed spaces, Adv. Difference Equ. 2012 (2012), Paper No. 141. [17] S.A. Mohiuddine and A. Alotaibi, Fuzzy stability of a cubic functional equation via fixed point technique, Adv. Difference Equ. 2012 (2012), Paper No. 48. [18] S.A. Mohiuddine and Q.M.D. Lohani, On generalized statistical convergence in intuitionistic fuzzy normed space, Chaos Solitons Fractals 42 (2009), 1731–1737. [19] S.A. Mohiuddine and H. Sevli, Stability of Pexiderized quadratic functional equation in intuitionistic fuzzy normed space, J. Comput. Appl. Math. 235 (2011), 2137–2146. [20] M. Mursaleen, S.A. Mohiuddine, and O.H.H. Edely, On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput. Math. Appl. 59 (2010), 603–611. [21] L. Narici and E. Beckenstein, Strange terrain-non-Archimedean spaces, Am. Math. Monthly 88 (1981), no. 9, 667–676. [22] C. Park, D. Boo, and Th. M. Rassias, Approximately additive mappings over p-adic fields, J. Chungcheong Math. Soc. 21 (2008), 1–14. [23] Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Am. Math. Soc. 72 (1978), 297–300. [24] R. Saadati and J. Park, On the intuitionistic fuzzy topological spaces, Chaos Solitons Fractals 27 (2006), 331–344. [25] S.M. Ulam, Problem in Modern Mathematics, Willey, New York, 1960. [26] M.R. Velayati and N. Salehi, Stability of maximum preserving functional equation on multi-Banach lattice by fixed point method, Fixed Point Theory 21 (2020), 363–373. [27] V.S. Vladimirov, I. V. Volovich and E. I. Zelenov, p-Adic Analysis and Mathematical Physics, World Scientific Publishing Co., Inc., River Edge, NJ, 1994. | ||
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