
تعداد نشریات | 21 |
تعداد شمارهها | 610 |
تعداد مقالات | 9,027 |
تعداد مشاهده مقاله | 67,082,769 |
تعداد دریافت فایل اصل مقاله | 7,656,171 |
Characterization and stability of multi-cubic mappings | ||
International Journal of Nonlinear Analysis and Applications | ||
مقاله 201، دوره 13، شماره 2، مهر 2022، صفحه 2493-2502 اصل مقاله (403.88 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.24314.2717 | ||
نویسندگان | ||
Ali Reza Neisi؛ Mohammad Sadegh Asgari* | ||
Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran | ||
تاریخ دریافت: 31 مرداد 1400، تاریخ بازنگری: 11 شهریور 1400، تاریخ پذیرش: 29 شهریور 1400 | ||
چکیده | ||
In this article, we introduce a new class of multi-cubic mappings and then unify a system of cubic functional equations defining a multi-cubic mapping to an equation, as multi-cubic functional equation. Moreover, we show that the mentioned equation describes the multi-cubic mappings. Furthermore, we prove the Hyers-Ulam stability of multi-cubic mappings in non-Archimedean normed spaces by applying a known fixed point theorem. | ||
کلیدواژهها | ||
Fixed point؛ Hyers-Ulam stability؛ non-Archimedean normed space؛ multi-cubic mapping | ||
مراجع | ||
[1] A. Bahyrycz, K. Ciepli´nski and J. Olko, On an equation characterizing multi-additive-quadratic mappings and its Hyers-Ulam stability. Appl. Math. Comput. 265 (2015), 448–455. [2] A. Bahyrycz, K. Ciepli´nski and J. Olko, On Hyers-Ulam stability of two functional equations in non-Archimedean spaces, J. Fixed Point Theory Appl. 2016 (2016), 18, 433–444. [3] A. Bodaghi, Functional inequalities for generalized multi-quadratic mappings, J. Inequal. Appl. 2021 (2021), Paper No. 145. [4] A. Bodaghi, Intuitionistic fuzzy stability of the generalized forms of cubic and quartic functional equations, J. Intel. Fuzzy Syst. 30 (2016), 2309–2317. [5] A. Bodaghi, I. A. Alias, L. Mousavi and S. Hosseini, Characterization and stability of multi mixed additive-quartic mappings: A fixed point application, J. Funct. Spaces. 2021 (2021), Art. ID 9943199, 11 pp. [6] A. Bodaghi and A. Fosner, Characterization, stability and hyperstability of multi-quadratic-cubic mappings, J. Inequal. Appl. 2021 (2021), Paper No. 49. [7] A. Bodaghi, S. M. Moosavi and H. Rahimi, The generalized cubic functional equation and the stability of cubic Jordan ∗-derivations, Ann. Univ. Ferrara. 59 (2013), 235–250. [8] A. Bodaghi, H. Moshtagh and H. Dutta, Characterization and stability analysis of advanced multi-quadratic functional equations, Adv. Diff. Equ. 2021 (2021), Paper No. 380. [9] A. Bodaghi, C. Park and S. Yun, Almost multi-quadratic mappings in non-Archimedean spaces, AIMS Math. 5 (2020), no. 5, 5230–5239. [10] A. Bodaghi, S. Salimi and G. Abbasi, Characterization and stability of multi-quadratic functional equations in non-Archimedean spaces, Ann. Uni. Craiova-Math. Comp. Sci. Ser. 48 (2021), no. 1, 88–97. [11] 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. [12] J. Brzd¸ek and K. Ciepli´nski, A fixed point approach to the stability of functional equations in non-Archimedean metric spaces, Nonlinear Anal. 74 (2011), 6861–6867. [13] K. Cieplinski, Generalized stability of multi-additive mappings, Appl. Math. Lett. 23 (2010), 1291–1294. [14] K. Cieplinski, On the generalized Hyers-Ulam stability of multi-quadratic mappings, Comput. Math. Appl. 62 (2011), 3418–3426. [15] K. Ciepli´nski, On Ulam stability of a functional equation, Results Math. 75 (2020), Paper No. 151. [16] K. Ciepli´nski, Ulam stability of functional equations in 2-Banach spaces via the fixed point method, J. Fixed Point Theory Appl. 23 (2021), Paper No. 33. [17] M. Dashti and H. Khodaei, Stability of generalized multi-quadratic mappings in Lipschitz spaces, Results Math. 74 (2019), Paper No. 163. [18] 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. [19] M.B. Ghaemi, M. Majani and M. Eshaghi Gordji, General system of cubic functional equations in non-archimedean spaces, Tamsui Oxford J. Inf. Math. Sci. 28 (2012), no. 4 ,407–423. [20] K. Hensel, Uber eine neue Begrndung der Theorie der algebraischen Zahlen, Jahresber. Dtsch. Math.-Ver. 6 (1897), 83–88. [21] K.W. Jun and H.M. Kim, The generalized Hyers-Ulam-Russias stability of a cubic functional equation, J. Math. Anal. Appl. 274 (2002), no. 2, 267–278. [22] K.W. Jun and H.M. Kim, On the Hyers-Ulam-Rassias stability of a general cubic functional equation, Math. Inequal. Appl. 6 (2003), no. 2, 289–302. [23] A. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Mathematics and its Applications, vol. 427, Kluwer Academic Publishers, Dordrecht, 1997. [24] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities. Cauchy’s Equation and Jensen’s Inequality, Birkhauser Verlag, Basel, 2009. [25] 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. [26] C.-G. Park, Multi-quadratic mappings in Banach spaces, Proc. Amer. Math. Soc. 131 (2002), 2501–2504. [27] J.M. Rassias, Solution of the Ulam stability problem for cubic mappings, Glas. Mat. Ser. III. 36 (2001), no. 1, 63–72. [28] S. Salimi and A. Bodaghi, A fixed point application for the stability and hyperstability of multi-Jensen-quadratic mappings, J. Fixed Point Theory Appl. 22 (2020), Paper No. 9. [29] S. Salimi and A. Bodaghi, Hyperstability of multi-mixed additive-quadratic Jensen type mappings, U.P.B. Sci. Bull., Series A. 82 (2020), no. 2, 55–66. [30] S.M. Ulam, Problems in Modern Mathematics, Science Editions, Wiley, New York, 1964. [31] T.Z. Xu, Stability of multi-Jensen mappings in non-Archimedean normed spaces, J. Math, Phys. 53 (2012), Art ID. 023507. [32] T.Z. Xu, C. Wang and Th.M. Rassias, On the stability of multi-additive mappings in non-Archimedean normed spaces. J. Comput. Anal. Appl. 18 (2015), 1102–1110. [33] X. Zhao, X. Yang and C.-T. Pang, Solution and stability of the multi quadratic functional equation, Abstr. Appl. Anal. 2013 (2013), Art. ID 415053, 8 pp. | ||
آمار تعداد مشاهده مقاله: 43,914 تعداد دریافت فایل اصل مقاله: 486 |