Affiliations: School of Science, Hubei University of Technology, Wuhan, Hubei, P.R. China
Correspondence:
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Corresponding author. Zhihua Wang, School of Science, Hubei University of Technology, Wuhan, Hubei 430068, P.R. China. E-mail: [email protected].
Note: [1] This research work is supported by the National Natural Science Foundation of China (Grant Nos. 11401190).
Abstract: Let k ≥ 2 be an integer. The purpose of this paper is first to introduce the notation of Felbin’s type fuzzy normed linear spaces, and then by virtue of this notation to study some stability results concerning the more general cubic functional equation of the form
f(x+ky)+f(x-ky)+f(kx)=k2f(x+y)+k2f(x-y)+(k3-2k2+2)f(x)
in the setting of Felbin’s type fuzzy normed linear spaces by employing the direct and fixed point methods. Then some applications of our results for the stability of the cubic functional equation from a real normed space to a Banach space will be demonstrated. Furthermore, the interdisciplinary relation between the theory of Felbin’s type fuzzy spaces and the theory of functional equations are also presented in this paper.
Keywords: Fixed point method, Felbin’s type fuzzy normed linear space, fuzzy real number, generalized Hyers-Ulam stability
