TY - JOUR T1 - Stability of Radical Cubic Functional Inequality in Modular Spaces and Fuzzy Banach Space AU - Baza, Abderrahman AU - Rossafi, Mohamed PY - 2024 DA - July JF - Azerbaijan Journal of Mathematics JO - AZJM PB - Azerbaycan Milli Bilimler Akademisi WT - DergiPark SN - 2218-6816 SP - 144 EP - 159 VL - 14 IS - 2 LA - en AB - The aim of this paper is to investigate the Hyers-Ulam stability of radicalcubic functional inequality in modular space with ∆2-condition and in fuzzy Banachspace KW - Hyers-Ulam stability KW - radical cubic functional inequality KW - modular spaces KW - fuzzy Banach space KW - ∆2-condition CR - [1] I. Amemiya, On the representation of complemented modular lattices, J. Math. Soc. Japan, 9(2), 1957, 263–279. CR - [2] Y. Aribou, S. Kabbaj, New functional inequality in non-Archimedean Banach spaces related to radical cubic functional equation, Asia Math., 2(3), 2018, 24–31. CR - [3] T. Bag, S.K. Samanta, Finite dimensional fuzzy normed linear space, J. Fuzzy Math., 11(2), 2003, 687–706. CR - [4] J.A. Baker, The stability of certain functional equations, Proc. Am. Math. Soc., 112(3), 1991, 729–732. CR - [5] L. Cadariu, V. Radu, Fixed Points and the Stability of Jensen’s Functional Equation, J. Inequalities Pure Appl., 4(4), 2003, 1–7. CR - [6] Y.J. Cho, C. Park, R. Saadati, Functional inequalities in non-Archimedean Banach spaces, Appl. Math. Lett., 23(10), 2010, 1238–1242. CR - [7] J.B. Diaz, B. Margolis, A Fixed Point Theorem of the Alternative, for Contractions on a Generalized Complete Metric Space, Bull. Am. Math. Soc., 74(2), 1968, 305–309. CR - [8] P. Gavruja, A generalization of the hyers-ulam-rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184(3), 1994, 431–436. CR - [9] D.H. Hyers, On the Stability of the Linear Functional Equation, Proc. Natl. Acad. Sci., 27(4), 1941, 222–224. CR - [10] M.A. Khamsi, Quasicontraction mappings in modular spaces without ∆2- condition, Fixed Point Theory Appl., 2008, 2008, 1-6. CR - [11] S. Koshi, T. Shimogaki, on F-Norms of Quasi-Modular Spaces, J. Fac. Sci., Hokkaido Univ., Ser. 1 , 15(3–4), 1961. CR - [12] M. Krbec, Modular Interpolation Spaces I, Zeitschrift F¨ur Anal. Und Ihre Anwendungen, 1(1), 1982, 25–40. CR - [13] W.A. Luxemburg, Banach function spaces, PhD Thesis, Delft University of Technology, Delft, The Netherlands, 1959. CR - [14] B. Mazur, Modular curves and the eisenstein ideal, Publ. Math´ematiques L’Institut Des Hautes Sci., 47(1), 1977, 33–186. CR - [15] D. Mihet, V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl., 343, 2008, 567-572. CR - [16] J. Musielak, Orlicz Spaces and Modular Spaces, Lect. Notes Math. 1034 Springer, Berlin, Germany, 1983. CR - [17] H. Nakano, Modulared Semi-Ordered Linear Spaces, Maruzen, Tokyo, Japan, 1950. CR - [18] W. Orlicz, Collected Papers, I, II, PWN, Warszawa, 1988. CR - [19] Z. P´ales, Generalized stability of the Cauchy functional equation, Aequationes Math., 56(3), 1998, 222–232. UR - https://dergipark.org.tr/en/pub/azerjmath/issue//1595080 L1 - https://dergipark.org.tr/en/download/article-file/4410994 ER -