Affiliations: School of Mathematics and Statistics, Tianshui Normal University, Tianshui, P.R. China | School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China | School of Information, Capital University of Economics and Business, Beijing, P.R. China | Department of Mathematics and Finance, Chongqing University of Arts and Sciences, Yongchuan, P.R. China
Note: [] Corresponding author. Yonghong Shen, School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, P.R. China; School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R. China. E-mails: shenyonghong2008@hotmail.com, chenwei@cueb.edu.cn (Wei Chen), yylan81@hotmail.com (Yaoyao Lan).
Abstract: In this paper, the concept of fuzzy quasi-β-normed spaces is introduced based on the continuous t-norm, which can be regarded as an extension of the fuzzy normed spaces and the quasi fuzzy normed spaces, respectively. Afterwards, a universal stability result in a fuzzy quasi-β-normed space under the strongest triangular norm $\top_M$ is established by employing the fixed point alternative theorem. Using this result, the fuzzy stability problem of a septic functional equation is examined.
