On the Stability of a k-Cubic Functional Equation in Intuitionistic Fuzzy n-Normed Spaces

Abstract

In this paper, we investigate some stability results concerning the k-cubic functional equation f (kx+y)+f (kx−y) = kf (x+y)+kf (x− y) + 2k(k 2 − 1)f (x) in the intuitionistic fuzzy n-normed spaces.Mathematics Subject Classification. Primary 46S40; Secondary 39B52, 39B82, 26E50, 46S50.

On Hyperstability of the Cauchy Functional Equation in n-Banach Spaces

“…Clearly, the case ι = 0 is exactly (28). Therefore, fix k ∈ N 0 and assume that ( 29) holds for ι = k. Then by ( 21), ( 26), (27) and the triangle inequality, we get…”

“…our Remark 2). More information on the n-normed spaces and some problems investigated in them (among others in fixed-point theory) can be found for instance in [15,[22][23][24][25][26][27][28].…”

Approximate fixed points for $n$-Linear functional by $(\mu,\sigma)$- nonexpansive Mappings on $n$-Banach spaces

“…For example, Batkunde et al, introduced the topological properties with respect to its quotient space of n-normed spaces, see ([5, 6, 7]). Basic properties, fuzzy cases and n-distance of n-normed spaces were found in ( [8,9,10]). Sequences on n-normed spaces were discussed by Ekariani et al in [11,12,13].…”

Multiquartic functional equations

“…In [12], the first author and Shojaee studied the Hyers-Ulam stability for multicubic mappings on normed spaces and also proved that a multicubic functional equation can be hyperstable, that is, every approximately multicubic mapping is multicubic. For other forms of cubic functional equations and their stabilities, we refer to [13][14][15][16][17][18].…”