[1] J. Aczel and J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, Cambridge, 1989.
[2] G. Alsahli and A. Bodaghi, A system of generalized quadratic functional equations and fuzzy difference results, Symmetry 17 (2025), 866.sym17060866.
[3] D. Amir, Characterizations of Inner Product Spaces, Dirkhauser-Verlag, Basel, 1986.
[4] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan. 2 (1950), 64–66.
[5] T. Bag and S.K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math. 11 (2003), 687–705.
[6] T. Bag and S.K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets Syst. 151 (2005), 513–547.
[7] R. Biswas, Fuzzy inner product spaces and fuzzy norm functions, Inform. Sci. 53 (1991), 185–190.
[8] A. Bodaghi, Functional inequalities for generalized multi-quadratic mappings, J. Inequ. Appl. 2021 (2021), 145.
[9] A. Bodaghi and I.A. Alias, Approximate ternary quadratic derivations on ternary Banach algebras and C∗-ternary rings, Adv. Differ. Equ. 2012 (2012), Paper No. 11.
[10] A. Bodaghi, I. A. Alias, and M. E. Gordji, On the stability of quadratic double centralizers and quadratic multipliers: A fixed point approach, J. Inequal. Appl. 2011 (2011), Art. ID 957541, 9 pp.
[11] A. Bodaghi, H. Moshtagh and H. Dutta, Characterization and stability analysis of advanced multi-quadratic functional equations, Adv. Differ. Equ. 2021, (2021), 380.
[12] A. Bodaghi, H. Moshtagh and A. Mousivand, Characterization and stability of multi-Euler-Lagrange quadratic functional equations, J. Func. Spaces. 2022 (2022), Art. ID 3021457, 9 pp.
[13] A. Bodaghi, C. Park, and S. Yun, Almost multi-quadratic mappings in non-Archimedean spaces, Aims Math. 5 (2020), no. 5.
[14] S.C. Cheng and J.M. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bull. Calcutta Math. Soc. 86 (1994), 429–436.
[15] K. Cieplinski, On the generalized Hyers-Ulam stability of multi-quadratic mappings, Comput. Math. Appl. 62 (2011), 3418–3426.
[16] S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg. 62 (1992), 59–64.
[17] J.B. Diaz and B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968), 305–309.
[18] M. Eshaghi Gordji and A. Bodaghi, On the Hyers-Ulam-Rassias stability problem for quadratic functional equations, East J. Approx. 16 (2010), no. 2, 123–130
[19] C. Felbin, Finite dimensional fuzzy normed linear spaces, Fuzzy Sets Syst. 48 (1992), 239–248.
[20] Z. Gajda, On stability of additive mappings, Int. J. Math. Math. Sci. 14, no. 3 (1991), 431–434.
[21] P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431–436.
[22] O. Hadzic, E. Pap, and V. Radu, Generalized contraction mapping principles in probabilistic metric spaces, Acta Math. Hung. 101 (2003), 131–148.
[23] D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. 27 (1941), 222–224.
[24] A.K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets Syst. 12 (1984), 143–154.
[25] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica 11 (1975), 326–334.
[26] S.V. Krishna and K.K.M. Sarma, Separation of fuzzy normed linear spaces, Fuzzy Sets Syst. 63 (1994), 207–217.
[27] D. Mihet and V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl. 343 (2008), no. 1, 567–572.
[28] A.K. Mirmostafaee, M. Mirzavaziri, and M.S. Moslehian, Fuzzy stability of the Jensen functional equation, Fuzzy Sets Syst. 159 (2008), 730–738.
[29] A.K. Mirmostafaee and M.S. Moslehian, Fuzzy approximately cubic mappings, Inf. Sci. 178 (2008), 3791–3798.
[30] A.K. Mirmostafaee and M.S. Moslehian, Fuzzy versions of Hyers-Ulam-Rassias theorem, Fuzzy Sets Syst. 159 (2008), 720–729.
[31] C. Park, Stability of the Cauchy-Jensen functional equation in fuzzy Banach algebras, Appl. Math. Lett. 24 (2011), 2024–2029.
[32] C.-G. Park, Multi-quadratic mappings in Banach spaces, Proc. Amer. Math. Soc. 131 (2002), 2501–2504.
[33] J. M. Rassias, On the stability of the general Euler-Lagrange functional equation, Demonstratio Math. 29 (1996), no. 4, 755–766.
[34] Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (2) (1978), 297–300.
[35] Th.M. Rassias, Functional Equations and Inequalities, Kluwer Academic Publishers, 2000.
[36] F. Skof, Proprieta locali e approssimazione di operatori, Rend. Sem. Mat. Fis. Milano, 53 (1983), 113–129.
[37] M. Turinici, Sequentially iterative processes and applications to Volterra functional equations, Ann. Uni. Mariae Curie-Sklodowska, Section-A. 32 (1978), 127–134.
[38] S.M. Ulam, Problems in Modern Mathematics, Science Editions, John Wiley & Sons, Inc., New York, 1964.
[39] J.Z. Xiao and X.H. Zhu, Fuzzy normed spaces of operators and its completeness, Fuzzy Sets Syst. 133 (2003), 389–399.
[40] C. Wu and J. Fang, Fuzzy generalization of Klomogoroff's theorem, J. Harbin Inst. Technol. 1 (1984), 1–7 (in Chinese, English abstract).
[41] T.-Z. Xu, Approximate multi-Jensen, multi-Euler-Lagrange additive and quadratic mappings in nn-Banach spaces, Abstr. Appl. Anal. 2013, Art. ID 648709, 12 pp.
[42] L. Zadeh, Fuzzy sets, Inf. Control. 8 (1965), 338–353.
[43] X. Zhao, X. Yang, and C.-T. Pang, Solution and stability of the multiquadratic functional equation, Abstr. Appl. Anal. 2013 (2013), Art. ID 415053, 8 pp.