Generalized Ulam–Hyers stability of (a, b; k > 0)-cubic functional equation in intuitionistic fuzzy normed spaces

Abstract

In this paper, we proved the general solution in vector space and established the generalized Ulam–Hyers stability of $$(a,b;k>0)-$$ cubic functional equation $$\begin{aligned} \frac{a+\sqrt{k}~b}{2} f\left( ax+\sqrt{k}~by\right)&+\frac{a-\sqrt{k}~b}{2} f\left( ax-\sqrt{k}~by\right) +k(a^2-kb^2)b^2f(y)\\&=k(ab)^2f(x+y)+(a^2-kb^2)a^2f(x) \end{aligned}$$ where $$a\ne \pm 1, 0; b\ne \pm 1, 0; k>0$$ in Banach space and Intuitionistic fuzzy normed spaces using both direct and fixed point methods.