Document Type : Research Paper

Authors

• H. Khodaei
• M. Kamyar

Department of Mathematics, Semnan University P. O. Box 35195-363, Semnan, Iran.

Abstract

Moslehian and Mirmostafaee, investigated the fuzzy stability problems for the Cauchy additive functional equation, the Jensen additive functional equation and the cubic functional equation in fuzzy Banach spaces.  In this paper, we investigate the generalized Hyers–-Ulam--Rassias stability of the generalized additive functional equation with $n$--variables, in fuzzy Banach spaces. Also, we will show that there exists a close relationship between the fuzzy continuity behavior of a fuzzy almost additive function, control function and the unique additive function which approximate the almost additive function.

Keywords

• Fuzzy stability
• Additive functional equation
• Fuzzy normed space