Abstract
In this paper, by using fixed point theory, we investigate the generalized Hyers–Ulam stability of an \(\alpha \)-cubic functional equation in modular spaces.
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Aoki, T.: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Japan 2, 64–66 (1950)
Bouikhalene, B., Eloqrachi, E.: Hyers-Ulam stability of spherical functions. Georgian Math. J. 23(2), 181–189 (2016)
Czerwik, S.: Functional equations and inequalities in several variables. World Scientific, New Jersey, London, Singapore, Hong Kong (2002)
Eskandani, G.Z., Rassias, J.M.: Approximation of general \(\alpha \)-cubic functional equations in 2-Banach spaces. Ukr. Math. J. 10, 1430–1436 (2017)
Eskandani, G.Z., Rassias, J.M., Gavruta, P.: Generalized Hyers-Ulam stability for a general cubic functional equation in quasi–normed spaces, Asian-Eur. J. Math. 4(03), 413–425 (2011)
Găvruta, P.: On a problem of G. Isac and Th. M. Rassias concerning the stability of mappings. J. Math. Anal. Appl. 261, 543–553 (2001)
Găvruta, P.: An answer to question of John M. Rassias concerning the stability of Cauchy equation, Advanced in Equation and Inequality, Edited by John M. Rassias, Hadronic Press Mathematics Series pp 67–71 (1999)
Găvruta, P.: A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings. J. Math. Anal. Appl. 184, 431–436 (1994)
Hyers, D.H.: On the stability of the linear functional equation. Proc. Nat. Acad. Sci. 27, 222–224 (1941)
Hyers, D.H., Isac, G., Rassias, Th.M: Stability of functional equations in several variables. Birkhäuser, Basel (1998)
Jung, S.M.: Hyers-Ulam-Rassias stability of functional equations in mathematical analysis. Hadronic Press, Palm Harbor (2001)
Nakano, H.: Modulared semi-ordered linear spaces. Maruzen, Tokyo, Japan (1950)
Khamsi, M. A.: Quasicontraction Mapping in modular spaces without \(\Delta _{2}\)-condition, Fixed Point Theory and Applications Volume, Artical ID 916187, 6 pages (2008)
Koshi, S., Shimogaki, T.: On F-norms of quasi-modular spaces. J. Fac. Sci. Hokkaido Univ. Ser. I 15(3), 202–218 (1961)
Park, C.: Homomorphisms between Poisson \(JC^{*}\)-algebras. Bull. Braz. Math. Soc. 36, 79–97 (2005)
Rassias, J.M.: On approximation of approximately linear mappings by linear mappings, J Funct Anal. 46(1), 126—130 (1982)
Rassias, J.M.: On approximation of approximately linear mappings by linear mappings. Bull. des Sci. Math. 108(4), 445–446 (1984)
Rassias, J.M.: Solution of a problem of Ulam. J. Approx. Theory 57(3), 268–273 (1989)
Rassias, J.M.: Solution of a stability problem of Ulam. Discussiones Mathematicae 12, 95–103 (1992)
Rassias, Th.M.: On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc. 72, 297–300 (1978)
Rassias, Th.M.: On a modified Hyers-Ulam sequence. J. Math. Anal. Appl. 158, 106–113 (1991)
Sadeghi, G.: A fixed point approach to stability of functional equations in modular spaces. Bull. Malaysian Math. Sci. Soc. 37, 333–344 (2014)
Ulam, S.M.: A collection of the mathematical problems, Interscience Publ. New York, 431–436 (1960)
Wongkum, K., Chaipunya, P., Kumam, P.: On the Generalized Ulam–Hyers–Rassias Stability of Quadratic Mappings in Modular Spaces without \(\Delta _{2}\)-Conditions, Journal of Function Spaces, Volume, Article ID 461719, 7 pages (2014)
Yamamuro, S.: On conjugate spaces of Nakano spaces. Trans. Amer. Math. Soc. 90, 291–311 (1959)
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The first author was supported by University of Tabriz.
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Eskandani, G.Z., Rassias, J.M. Stability of general A-cubic functional equations in modular spaces. RACSAM 112, 425–435 (2018). https://doi.org/10.1007/s13398-017-0388-5
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DOI: https://doi.org/10.1007/s13398-017-0388-5