پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 677 |
| تعداد مقالات | 9,874 |
| تعداد مشاهده مقاله | 70,021,530 |
| تعداد دریافت فایل اصل مقاله | 49,294,005 |
Superstability of the $p$-radical sine functional equation | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 14، دوره 14، شماره 4، تیر 2023، صفحه 161-170 اصل مقاله (424.28 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6567 | ||
| نویسندگان | ||
| Gwang Hui Kim* 1؛ Madjid Eshaghi Gordji2 | ||
| 1Department of Mathematics, Kangnam University, Giheung-gu, Yongin-si, Gyeonggi-do, 16979, Repub. of Korea | ||
| 2Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran | ||
| تاریخ دریافت: 27 آذر 1400، تاریخ بازنگری: 09 اردیبهشت 1401، تاریخ پذیرش: 18 اردیبهشت 1401 | ||
| چکیده | ||
| In this paper, we investigate the transferred superstability of the $p$-radical functional equation \begin{equation*} f\left(\sqrt[p]{\frac{x^{p}+y^{p}}{2}}\right)^{2} -f\left(\sqrt[p]{\frac{x^{p}-y^{p}}{2}}\right)^{2} =f(x)f(y) \end{equation*} with respect to the sine functional quation from the Pexider type $p$-radical functional equation $f\left(\sqrt[p]{x^{p}+y^{p}}\right) +g\left(\sqrt[p]{x^{p}-y^{p}}\right)=\lambda \cdot h(x)k(y)$, where $p$ is an odd positive integer and $f$ is a complex valued function. Furthermore, the results are applied to the stability of the cosine type $p$-radical functional equations. | ||
| کلیدواژهها | ||
| superstability؛ $p$-radical equation؛ cosine functional equation؛ sine functional equation؛ Wilson equation؛ Kim equation | ||
| مراجع | ||
|
[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 and 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 and R. Ger, On some trigonometric functional inequalities, Functional Equations- Results and Advances (2002), 3–15. [6] J.A. Baker, The stability of the cosine equation, Proc. Amer. Math. Soc. 80 (1980), 411–416. [7] J.A. Baker, J. Lawrence and F. Zorzitto, The stability of the equation f(x + y) = f(x)f(y), Proc. Amer. Math. Soc. 74 (1979), 242–246. [8] B. Bouikhalene, E. Elquorachi and 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. Amer. Math. Soc. 88 (1983), 631–634. [11] Iz. EL-Fassi, S. Kabbaj and G.H. Kim, Superstability of a Pexider-type trigonometric functional equation in normed algebras, Int. J. Math. Anal. 9 (2015), no. 58, 2839–2848. [12] P. Gˇavruta, On the stability of some functional equations, Th. M. Rassias and J. Tabor, Stability of mappings of Hyers-Ulam type, Hadronic Press, 1994, pp. 93–98. [13] M. Eshaghi Gordji and M. Parviz, On the Hyers-Ulam-Rassias stability of the functional equation f( p x 2 + y2) = f(x) + f(y), Nonlinear Funct. Anal. Appl. 14 (2009), 413–420. [14] D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. 27 (1941), 222–224. [15] Pl. Kannappan, Functional equations and inequailitis with applications, Springer, 2009. [16] Pl. Kannappan and G.H. Kim, On the stability of the generalized cosine functional equations, Ann. Acad. Pedagog. Crac. Stud. Math. 1 (2001), 49–58. [17] G.H. Kim, Superstability of the p-radical functional equations related to Wilson and Kim’s equation, Int. J. Nonlinear Anal. Appl. 12 (2021), 571–582. [18] G.H. Kim, Superstability and solution of the pexiderized trigonometric functional equation, Math. Statist. 8 (2020), 363–371. [19] G.H. Kim, On the superstability of the pexider type trigonometric functional equation, J. Inequal. Appl. 2010 (2010), Doi:10.1155/2010/897123. [20] G.H. Kim, On the Stability of the generalized sine functional equations, Acta Math. Sin., Engl. Ser. 25 (2009), 965–972 [21] G.H. Kim, The Stability of the d’Alembert and Jensen type functional equations, J. Math. Anal Appl. 325 (2007), 237–248. [22] G.H. Kim, A Stability of the generalized sine functional equations, J. Math. Anal. Appl. 331 (2007), 886–894. [23] G.H. Kim and Y.H. Lee, boundedness of approximate trigonometric functional equations, Appl. Math. Lett. 331 (2009), 439–443. [24] Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300. [25] S. M. Ulam, “Problems in Modern Mathematics” Chap. VI, Science editions, Wiley, New York, 1964 | ||
|
آمار تعداد مشاهده مقاله: 16,611 تعداد دریافت فایل اصل مقاله: 8,188 |
||