Fuzzy stability for a class of cubic functional equations

Article type: Research Article

Authors: Kim, Chang Il | Han, Giljun^{; *}

Affiliations: Department of Mathematics Education, Dankook University, Gyeonggi-do, Korea

Correspondence: [*] Corresponding author. Giljun Han, Department of Mathematics Education, Dankook University, 152, Jukjeon-ro, Suji-gu, Yongin-si, Gyeonggi-do, 448-701, Korea. E-mail: gilhan@dankook.ac.kr.

Abstract: In this paper, we investigate the following typical form of a class of cubic functional equations: f(x+2y)-3f(x+y)+3f(x)-f(x-y)-6f(y)  +k[f(mx+y)+f(mx-y)-m[f(x+y)+f(x-y)]-2(m3-m)f(x)]=0 for some rational number m and some real number k. Furthermore, we provide a systematic program to prove the generalized Hyers-Ulam stability for the class of functional equations via the stability for the typical form in fuzzy normed spaces.

Keywords: Fuzzy Banach space, fixed point theorem, stability, cubic mapping

DOI: 10.3233/JIFS-17674

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3779-3787, 2017