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An additive $(u, \beta)$-functional equation and linear mappings in Banach modules | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 140، دوره 13، شماره 2، مهر 2022، صفحه 1747-1755 اصل مقاله (410.69 K) | ||
| نوع مقاله: Special issue editorial | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.22580.2386 | ||
| نویسندگان | ||
| Siriluk Paokanta1؛ Choonkil Park2؛ Jung Rye Lee* 3 | ||
| 1Department of Mathematics, Hanyang University, Seoul 04763, Korea | ||
| 2Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea | ||
| 3Department of Data Science, Daejin University, Kyunggi 11159, Korea | ||
| تاریخ دریافت: 17 بهمن 1399، تاریخ بازنگری: 26 بهمن 1399، تاریخ پذیرش: 23 اسفند 1399 | ||
| چکیده | ||
| Let $A$ be a unital $C^*$-algebra. In this paper, we investigate the additive $(u, \beta)$-functional equation \begin{eqnarray}\label{0.1} f(x)+ u^* f(u y)+ f( z) = \beta^{-1} f(\beta(x+y+z)) \end{eqnarray} for all unitary elements $u$ in $A$ and for a fixed nonzero complex number $\beta$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive $(u, \beta)$-functional equation (\ref{0.1}) in Banach modules. | ||
| کلیدواژه‌ها | ||
| Hyers-Ulam stability؛ additive $(u, beta)$-functional equation؛ $A$-linear mapping؛ fixed point method؛ direct method؛ Banach module | ||
| 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] B. Belaid and E. Elhoucien, Solutions and stability of a generalization of Wilson’s equation, Acta Math. Sci. Ser. B Engl. Ed. 36 (2016), 791–80[3] L. C˘adariu and V. Radu, Fixed points and the stability of Jensen’s functional equation, J. Inequal. Pure Appl. Math. 4, no. 1, Art. ID 4 (2003). [4] L. C˘adariu and V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, Grazer Math. Ber. 346 (2004), 43–52. [5] L. C˘adariu and V. Radu, Fixed point methods for the generalized stability of functional equations in a single variable, Fixed Point Theory Appl. 2008, Art. ID 749392 (2008). [6] A. Chahbi and N. Bounader, On the generalized stability of d’Alembert functional equation, J. Nonlinear Sci. Appl. 6 (2013), 198–204. [7] J. 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. [8] G. Z. Eskandani and P. Gˇavruta, Hyers-Ulam-Rassias stability of pexiderized Cauchy functional equation in 2- Banach spaces, J. Nonlinear Sci. Appl. 5 (2012), 459–465. [9] P. Gˇavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431–43. [10] A. Ghaffari, Module homomorphisms associated with Banach algebras, Taiwanese J. Math. 15 (2011), 1075–1088. [11] S.G. Ghaleh and K. Ghasemi, Stability of n-Jordan ∗-derivations in C ∗ -algebras and JC∗ -algebras, Taiwanese J. Math. 16 (2012), 1791–1802. [12] A. Gil´anyi, Eine zur Parallelogrammgleichung ¨aquivalente Ungleichung, Aequationes Math. 62 (2001), 303–309. [13] A. Gil´anyi, On a problem by K. Nikodem, Math. Inequal. Appl. 5 (2002), 707–710. [14] D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222–224. [15] G. Isac and Th.M. Rassias, Stability of ψ-additive mappings: Applications to nonlinear analysis, Internat. J. Math. Math. Sci. 19 (1996), 219–228. [16] R.V. Kadison and G. Pedersen, Means and convex combinations of unitary operators, Math. Scand. 57 (1985), 249–266. [17] D. Mihet¸ and V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl. 343 (2008), 567–572. [18] C. Park, Homomorphisms between Poisson JC∗ -algebras, Bull. Braz. Math. Soc. 36 (2005), 79–97. [19] C. Park, Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras, Fixed Point Theory Appl. 2007, Art. ID 50175 (2007). [20] C. Park, Orthogonal stability of a cubic-quartic functional equation, J. Nonlinear Sci. Appl. 5 (2012), 28–36. [21] C. Park, Quadratic ρ-functional inequalities in Banach spaces, Acta Math. Sci. Ser. B Engl. Ed. 35 (2015), 1501–1510. [22] V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory 4 (2003), 91–96. [23] Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300. [24] S.M. Ulam, A Collection of the Mathematical Problems, Interscience Publ. New York, 1960. | ||
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