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A remark on the Hyers-Ulam-Rassias stability of $n$-Jordan $*$-homomorphisms on $C^*$-algebras | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 1، دوره 15، شماره 4، تیر 2024، صفحه 1-9 اصل مقاله (376.61 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29835.4272 | ||
| نویسنده | ||
| Ismail Nikoufar* | ||
| Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| تاریخ دریافت: 17 بهمن 1401، تاریخ بازنگری: 23 بهمن 1401، تاریخ پذیرش: 31 فروردین 1402 | ||
| چکیده | ||
| In the Hyers-Ulam-Rassias stability depending on the type of the function whose stability we want to verify a suitable functional equation is used. The authors in [6] want to investigate the Hyers-Ulam-Rassias stability of $n$-Jordan $C^*$-homomorphisms on $C^*$-algebras, but they used a quadratic functional equation while we know that the homomorphisms are linear on $C^*$-algebras. In this paper, we correct the main results of [6] by removing the quadratic functional equation and replacing the linear one and removing some extra conditions. We also show that by using some other multi-variable linear functional equations, the estimation becomes better and more accurate. | ||
| کلیدواژهها | ||
| Hyers-Ulam-Rassias stability؛ $n$-jordan $C^*$-homomorphism؛ $n$-jordan homomorphism؛ $C^*$-algebra | ||
| مراجع | ||
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[1] P.W. Cholewa, Remarks on the stability of functional equations, Aequationes Math. 27 (1984), 76–86. [2] S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Semin. Univ. Hambg. 62 (1992), 59–64. [3] S. Czerwik and K. Dlutek, Stability of the quadratic functional equation in Lipschitz spaces, J. Math. Anal. Appl. 293 (2004), 79–88. [4] A. Ebadian, I. Nikoufar, Th.M. Rassias, and N. Ghobadipour, Stability of generalized derivations on Hilbert C∗-modules associated to a Pexiderized Cauchy-Jensen type functional equation, Acta Math. Sci. 32B (2012), 1226–1238. [5] S.-M. Jung and P.K. Sahoo, Hyers-Ulam stability of the quadratic equation of Pexider type, J. Korean Math. Soc. 38 (2001), 645–656. [6] S. Ghaffary Ghaleh and K. Ghasemi, Hyers-Ulam-Rassias stability of n-Jordan ∗-homomorphisms on C∗-algebras, Bull. Iranian Math. Soc. 39 (2013), 347–353. [7] M.E. Gordji, n-Jordan homomorphisms, Bull. Austral. Math. Soc. 80 (2009), 159–164. [8] M.E. Gordji, A. Jabbari, and E. Kapapinar, Automatic continuity of surjective n-homomorphisms on Banach algebras, Bull. Iran. Math. Soc. 41 (2015), 1207–1211. [9] M.E. Gordji, T. Karimi, and S.K. Gharetapeh, Approximately n-Jordan homomorphisms on Banach algebras, J. Ineq. Appl. 870843 (2009). [10] H. Khodaei and Th.M. Rassias, Approximately generalized additive functions in several variables, Int. J. Nonlinear Anal. Appl. 1 (2010), 22–41. [11] H. Khodaei, Asymptotic behavior of n-Jordan homomorphisms, Mediterr. J. Math. 17, 143 (2020). [12] J.R. Lee, S.-Y. Jang, C. Park, and D.Y. Shin, Fuzzy stability of quadratic functional equations, Adv. Difference Equ. 2010 (2010), Article ID 412160, 16 pages. [13] J.B. Diaz and B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968), 305–309. [14] M.S. Moslehian, K. Nikodem, and D. Popa, Asymptotic aspect of the quadratic functional equation in multi-normed spaces, J. Math. Anal. Appl. 355 (2009), 717–724. [15] I. Nikoufar, Jordan (θ, ϕ)-derivations on Hilbert C∗-modules, Indag. Math. (N.S.) 26 (2015), 421–430. [16] I. Nikoufar, Refined almost double derivations and Lie ∗-double derivations, Miskolc Math. Notes 16 (2015), 1063–1071. [17] I. Nikoufar, Lipschitz criteria for bi-quadratic functional equations, Commun. Korean Math. Soc. 31 (2016), 819–825. [18] I. Nikoufar, Approximate tri-quadratic functional equations via Lipschitz conditions, Math. Bohemica 142 (2017), 337–344. [19] I. Nikoufar, Stability of multi-quadratic functions in Lipschitz spaces, Iran J. Sci. Tech. 43 (2019), 621–625. [20] C. Park, On the stability of the quadratic mapping in Banach modules, J. Math. Anal. Appl. 276 (2002), 135–144. [21] F. Skof, Local properties and approximations of operators, Rend. Sem. Mat. Fis. Milano 53 (1983), 113–129. | ||
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