Fuzzy HUR stability of partitioned functional equations

Sharifi, Alireza; Azadi Kenary, Hassan

doi:10.22075/ijnaa.2023.27677.3679

اداره چاپ و انتشارات دانشگاه سمنان

تعداد نشریات	21
تعداد شماره‌ها	610
تعداد مقالات	9,026
تعداد مشاهده مقاله	67,082,726
تعداد دریافت فایل اصل مقاله	7,656,156

	Fuzzy HUR stability of partitioned functional equations
International Journal of Nonlinear Analysis and Applications
مقاله 5، دوره 14، شماره 7، مهر 2023، صفحه 57-72 اصل مقاله (451.22 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.27677.3679
نویسندگان
Alireza Sharifi^* ¹؛ Hassan Azadi Kenary²
¹Department of Mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran Iran
²Department of Mathematics, Yasouj University, Yasouj, Iran
تاریخ دریافت: 10 تیر 1401، تاریخ بازنگری: 29 بهمن 1401، تاریخ پذیرش: 27 فروردین 1402
چکیده
In this paper, we establish the Hyers-Ulam-Rassias stability of the following functional equation $$ (4p)^nf\left(\frac{x_1+\cdots +x_{(4p)^n}}{(4p)^n}\right) + 4p\sum_{i=1}^{(4p)^{n-1}} f\left(\frac{x_{4pi-4p+1} + \cdots +x_{4pi}}{4p}\right) = 2 \sum_{i=1}^{(4p)^n} f\left(\frac{x_i+x_{i+1}}{2}\right) $$ in fuzzy Banach spaces.
کلیدواژه‌ها
Fuzzy relations؛ Analysis؛ Hyers-Ulam-Rassias stability؛ Fuzzy normed space

مراجع
[1] T. Bag and S.K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math. 11 (2003), 687–705. [2] T. Bag and S.K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets Syst. 151 (2005), 513–547. [3] R. Biswas, Fuzzy inner product spaces and fuzzy norm functions, Inf. Sci. 53 (1991), 185–190. [4] S.C. Cheng and J.N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bull. Calcutta Math. Soc. 86 (1994), 429–436. [5] P.W. Cholewa, Remarks on the stability of functional equations, Aequationes Math. 27 (1984), 76–86. [6] S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hambourg 62 (1992), 239–248. [7] H. Dutta, B.V.S. Kumar and S. Sabarinathan, Fuzzy stability of a new Hexic functional equation in various spaces, An. St. Univ. Ovidius Constanta 30 (2022), no. 3, 143–171. [8] M. Eshaghi Gordji and M. Bavand Savadkouhi, Stability of mixed type cubic and quartic functional equations in random normed spaces, J. Inequal. Appl. 2009 (2009), Article ID 527462. [9] M. Eshaghi Gordji, M. Bavand Savadkouhi and C. Park, Quadratic-quartic functional equations in RN-spaces, J. Inequal. Appl. 2009 (2009), Article ID 868423. [10] M. Eshaghi Gordji and H. Khodaei, Stability of Functional Equations, Lap Lambert Academic Publishing, London, United Kingdom, 2010. [11] M. Eshaghi Gordji, S. Zolfaghari, J.M. Rassias and M.B. Savadkouhi, Solution and stability of a mixed type cubic and quartic functional equation in quasi-Banach spaces, Abst. Appl. Anal. 2009 (2009), Article ID 417473. [12] C. Felbin, Finite-dimensional fuzzy normed linear space, Fuzzy Sets Syst. 48 (1992), 239–248. [13] Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci. 14 (1991), 431–434. [14] P. Gˇavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431–436. [15] D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222–224. [16] S. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, 2001. [17] A.K. Katsaras, Fuzzy topological vector spaces, Fuzzy Sets Syst. 12 (1984), 143–154. [18] I. Karmosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica 11 (1975), 326–334. [19] S.V. Krishna and K.K.M. Sarma, Separation of fuzzy normed linear spaces, Fuzzy Sets Syst. 63 (1994), 207–217. [20] R. Liu and D. O’Regan, Ulam type stability of first-order linear impulsive fuzzy differential equations, Fuzzy Sets Syst. 400 (2020), 34–89. [21] D. Mihet, The fixed point method for fuzzy stability of the Jensen functional equation, Fuzzy Sets Syst. 160 (2009), no. 11, 1663–1667. [22] 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. [23] A.K. Mirmostafaee, A fixed point approach to almost quartic mappings in quasi fuzzy normed spaces, Fuzzy Sets Syst. 160 (2009), no. 11, 1653–1662. [24] A.K. Mirmostafaee and M.S. Moslehian, Fuzzy approximately cubic mappings, Inf. Sci. 178 (2008), no. 19, 3791–3798. [25] A.K. Mirmostafaee and M.S. Moslehian, Fuzzy almost quadratic functions, Results Math. 52 (2008), no. 1-2, 161–177. [26] A.K. Mirmostafaee, M. Mirzavaziri and M.S. Moslehian, Fuzzy stability of the Jensen functional equation, Fuzzy Sets Syst. 159 (2008), no. 6, 730–738. [27] A.K. Mirmostafaee and M.S. Moslehian, Fuzzy versions of Hyers-Ulam-Rassias theorem, Fuzzy Sets Syst. 159 (2008), no. 6, 720–729. [28] E. Movahednia and M. Mursaleen, Stability of a generalized quadratic functional equation in intuitionistic fuzzy 2-normed space, Filomat 13 (2016), 449–457. [29] M. Mursaleen and K.J. Ansari, Stability results in intuition fuzzy normed spaces for a cubic functional equation, Appl. Math. Inf. Sci. 5 (2013), 1677–1684. [30] C. Park, On the stability of the linear mapping in Banach modules, J. Math. Anal. Appl. 275 (2002), 711–720. [31] C. Park, Modefied Trif ’s functional equations in Banach modules over a C∗-algebra and approximate algebra homomorphism, J. Math. Anal. Appl. 278 (2003), 93–108. [32] C. Park, Fuzzy stability of a functional equation associated with inner product spaces, Fuzzy Sets Syst. 160 (2009), 1632–1642. [33] C. Park, Linear functional equations in Banach modules over a C∗-algebra, Acta Appl. Math. 77 (2003), 125–161. [34] C. Park, D.Y. Shin, R. Saadati and J.R. Lee, Fixed point approach to the fuzzy stability of an AQCQ-functional equation, Filomat 30 (2016), no. 7, 1833–1851. [35] M. Ramdoss, D. Pachaiyappan, C. Park and J.R. Lee, Stability of a generalized n-variable mixed-type functional equation in fuzzy modular spaces, J. Inequal. Appl. 2021 (2021), no. 61, doi:10.1186/s13660-021-02594-y. [36] Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300. [37] Th.M. Rassias, On the stability of the quadratic functional equation and it’s application, Studia Univ. Babes Bolyai 43 (1998), 89–124. [38] Th.M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), 264–284. [39] Th.M. Rassias and P. ˇSemrl, On the Hyers-Ulam stability of linear mappings, J. Math. Anal. Appl. 173 (1993), 325–338. [40] W. Ren, Z. Yang, X. Sun and M. Qi, Hyers-Ulam stability of Hermite fuzzy differential equations and fuzzy Mellin transform, J. Intell. Fuzzy Syst. 35 (2018), no. 3, 3721–3731. [41] R. Saadati and C. Park, Non-Archimedean L-fuzzy normed spaces and stability of functional equations, Compu. Math. Appl. (2010), 2488–2496. [42] R. Saadati, M. Vaezpour and Y.J. Cho, A note to paper “On the stability of cubic mappings and quartic mappings in random normed spaces”, J. Inequal. Appl. 2009 (2009), Article ID 214530. [43] R. Saadati, S. Sedghi and H. Zhou, A common fixed point theorem for ψ-weakly commuting maps in L-fuzzy metric spaces, Iran. J. Fuzzy Syst. 5 (2008), no. 1, 47–53. [44] R. Saadati, M. M. Zohdi and S. M. Vaezpour, Nonlinear L-random stability of an ACQ functional equation, J. Inequal. Appl. 2011 (2011), Article ID 194394. [45] P. Seo, S. Lee and R. Saadati, Fuzzy stability of an additive-quadratic functional equation with the fixed point alternative, Pure and Appl. Math. 22 (2015), no. 3, 285–298. [46] A. Sharifi, H. Azadi, B. Yousefi and R. Soltani, HUR-approximation of an ELTA functional equation, Filomat 34 (2020), no. 13, 4311–4328. [47] F. Skof, Local properties and approximation of operators, Rend. Sem. Mat. Fis. Milano 53 (1983), 113–129. [48] T. Trif, On the stability of a functional equation deriving from an inequality of T. Popoviciu for convex functions, J. Math. Anal. Appl. 272 (2002), 604–616. [49] S.M. Ulam, Problems in Modern Mathematics, John Wiley and Sons, New York, NY, USA, 1964. [50] J. Wu and L. Lu, Hyers-Ulam-Rassias stability of additive mappings in fuzzy normed spaces, J. Math. 2021 (2021), Article ID 5930414. [51] Z. Zamani, B. Yousefi, and H. Azadi, Fuzzy Hyers-Ulam-Rassias stability for generalized additive functional equations, Bol. Soc. Paran. Mat. 40 (2022), no. 3s, 1–14.
آمار تعداد مشاهده مقاله: 16,509 تعداد دریافت فایل اصل مقاله: 208

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

پیوندهای مفید

آمار

Fuzzy HUR stability of partitioned functional equations