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An example for the nonstability of multicubic mappings | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 23، دوره 14، شماره 3، خرداد 2023، صفحه 273-277 اصل مقاله (344.79 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.25878.3150 | ||
| نویسنده | ||
| Abasalt Bodaghi* | ||
| Department of Mathematics, West Tehran Branch, Islamic Azad University, Tehran, Iran | ||
| تاریخ دریافت: 21 دی 1400، تاریخ بازنگری: 15 شهریور 1401، تاریخ پذیرش: 18 شهریور 1401 | ||
| چکیده | ||
| In this paper, we present a counterexample for the nonstability of multicubic mappings. In other words, we show that Corollary 3.5 of [A. Bodaghi and B. Shojaee, On an equation characterizing multi-cubic mappings and its stability and hyperstability, Fixed Point Theory. 22 (2021), No. 1, 83--92] does not hold when $\alpha=3n$. | ||
| کلیدواژهها | ||
| Banach space؛ Hyers-Ulam stability؛ multicubic mapping | ||
| مراجع | ||
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[1] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan. 2 (1950), 64–66.
[2] A. Bodaghi, Equalities and inequalities for several variables mappings, J. Inequal. Appl. 2022 (2022), Paper No. 6.
[3] A. Bodaghi and B. Shojaee, On an equation characterizing multi-cubic mappings and its stability and hyperstability, Fixed Point Theory 22 (2021), no. 1, 83–92.
[4] N. Ebrahimi Hoseinzadeh, A. Bodaghi and M.R. Mardanbeigi, Almost multi-cubic mappings and a fixed point application, Sahand Commun. Math. Anal. 17 (2020), no. 3, 131–143.
[5] Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci. 14 (1991), 431–434.
[6] M.B. Ghaemi, M. Majani and M. Eshaghi Gordji, General system of cubic functional equations in nonArchimedean spaces, Tamsui Oxford J. Inf. Math. Sci. 28 (2012), no. 4, 407–423.
[7] D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222–224.
[8] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities. Cauchy’s Equation and Jensen’s Inequality, Birkh¨auser Verlag, Basel, 2009.
[9] C. Park and A. Bodaghi, Two multi-cubic functional equations and some results on the stability in modular spaces, J. Inequal. Appl. 2020 (2020), Paper No. 6. https://doi.org/10.1186/s13660-019-2274-5
[10] Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72(2) (1978), no. 2, 297–300.
[11] S.M. Ulam, Problems in Modern Mathematics, Science Editions, Wiley, New York, 1964. | ||
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