Fuzzy approximate m-mappings in quasi fuzzy normed spaces

Abstract

Let 1≤m≤4 be a fixed integer and let f:X→Y be a mapping with X,Y two real vector spaces. For any fixed integers a with a≠0,±1, the following functional equationf(ax+y)+f(ax−y)=am−2[f(x+y)+f(x−y)]+2(a2−1)[am−2f(x)+(m−2)(1−(m−2)2)6f(y)] is said to be additive when m=1, quadratic when m=2, cubic when m=3 and quartic when m=4, respectively. For convenience, a solution of the above functional equation will be called an m-mapping. In this paper, for each m=1,2,3,4, we apply the fixed point method to investigate Hyers-Ulam stability results concerning the above functional equation in quasi fuzzy p-normed spaces. We also discuss the fuzzy continuity behavior of fuzzy approximate m-mappings in quasi fuzzy p-normed spaces. As applications, we establish Hyers-Ulam stability results of approximate m-mappings from a linear space into a quasi p-normed space.