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Superstability of the $p$-radical functional equations related to Wilson's and Kim's equation | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، Special Issue، اسفند 2021، صفحه 571-582 اصل مقاله (161.15 K) | ||
| نوع مقاله: Special issue editorial | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23376.2526 | ||
| نویسنده | ||
| Gwang Hui Kim* | ||
| Department of Mathematics, Kangnam University, Yongin, Gyeonggi, 16979, Republic of Korea | ||
| تاریخ دریافت: 19 اردیبهشت 1400، تاریخ پذیرش: 23 تیر 1400 | ||
| چکیده | ||
| In this paper, we solve and investigate the superstability of the $p$-radical functional equations related to the following Wilson and Kim functional equations \begin{align*} f\left(\sqrt[p]{x^{p}+y^{p}}\right) &+f\left(\sqrt[p]{x^{p}-y^{p}}\right)=\lambda f(x) g(y),\\ f\left(\sqrt[p]{x^{p}+y^{p}}\right) &+f\left(\sqrt[p]{x^{p}-y^{p}}\right)=\lambda g(x) f(y), \end{align*} where $p$ is an odd positive integer and $f$ is a complex valued function. Furthermore, the results are extended to Banach algebras. | ||
| کلیدواژهها | ||
| stability؛ superstability؛ radical functional equation؛ cosine functional equation؛ Wilson functional equation؛ Kim functional equation | ||
| مراجع | ||
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es [1] J. d’Alembert, Memoire sur les Principes de Mecanique, Hist. Acad. Sci. Paris, (1769), 278–286 [2] M. Almahalebi, R. El Ghali, S. Kabbaj, C. Park, Superstability of p-radical functional equations related to Wilson– Kannappan–Kim functional equations, Results Math. 76 (2021), Paper No. 97. [3] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950), 64–66. [4] R. Badora, On the stability of cosine functional equation, Rocznik Naukowo-Dydak. Prace Mat. 15 (1998), 1–14. [5] R. Badora, R. Ger, On some trigonometric functional inequalities, in Functional Equations- Results and Advances, 2002, pp. 3–15. [6] J. A. Baker, The stability of the cosine equation, Proc. Am. Math. Soc. 80 (1980), 411–416. [7] J. A. Baker, J. Lawrence, F. Zorzitto, The stability of the equation f(x + y) = f(x)f(y), Proc. Am. Math. Soc. 74 (1979), 242–246. [8] B. Bouikhalene, E. Elqorachi, J. M. Rassias, The superstability of d’Alembert’s functional equation on the Heisenberg group, Appl. Math. Lett. 23 (2010), 105–109. [9] D. G. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J. 16, (1949), 385–397. [10] P. W. Cholewa, The stability of the sine equation, Proc. Am. Math. Soc. 88 (1983), 631–634. [11] Iz. EL-Fassi, S. Kabbaj, G. H. Kim, Superstability of a Pexider-type trigonometric functional equation in normed algebras, Inter. J. Math. Anal. 9 (58), (2015), 2839–2848. [12] M. Eshaghi Gordji, M. Parviz, On the Hyers-Ulam-Rassias stability of the functional equation f( p x 2 + y 2) = f(x) + f(y), Nonlinear Funct. Anal. Appl. 14, (2009), 413–420. [13] P. Gǎvruta, On the stability of some functional equations, Th. M. Rassias and J. Tabor (eds.), Stability of mappings of Hyers-Ulam type, Hadronic Press, New York, 1994, pp. 93–98. [14] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA 27 (1941), 222–[15] Pl. Kannappan, The functional equation f(xy) + f(xy−1 ) = 2f(x)f(y) for groups, Proc. Am. Math. Soc. 19 (1968), 69–74. [16] Pl. Kannappan, Functional Equations and Inequailitis with Applications, Springer, New York, 2009. [17] Pl. Kannappan, G. H. Kim, On the stability of the generalized cosine functional equations, Ann. Acad. Pedagog. Crac. Stud. Math. 1 (2001), 49–58. [18] G. H. Kim, The stability of the d’Alembert and Jensen type functional equations, J. Math. Anal. Appl. 325 (2007), 237–248. [19] G. H. Kim, The stability of pexiderized cosine functional equations, Korean J. Math. 16 (2008), 103–114. [20] G. H. Kim, Superstability of some Pexider-type functional equation, J. Inequal. Appl. 2010 (2010), Article ID 985348. doi:10.1155/2010/985348. [21] G. H. Kim, S. H. Lee, Stability of the d’Alembert type functional equations, Nonlinear Funct. Anal. Appl. 9 (2004), 593–604. [22] G. H. Kim, Y. H. Lee, The superstability of the Pexider type trigonometric functional equation, Aust. J. Math. Anal. 7 (2011), Issue 2, 1–10. [23] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Am. Math. Soc. 72 (1978), 297–300. [24] S. M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1964. | ||
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