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In this paper, we proved the general solution in vector space and established the generalized Ulam–Hyers stability of $$(a,b;k>0)-$$ ( a , b ; k > 0 ) - cubic functional equation $$\begin{aligned} \frac{a+\sqrt{k}~b}{2} f\left( ax+\sqrt{k}~by\right)&+\frac{a-\sqrt{k}~b}{2} f\left( ax-\sqrt{k}~by\right) +k(a^2-kb^2)b^2f(y)\\&=k(ab)^2f(x+y)+(a^2-kb^2)a^2f(x) \end{aligned}$$ a + k b 2 f a x + k b y + a - k b 2 f a x - k b y + k ( a 2 - k b 2 ) b 2 f ( y ) = k ( a b ) 2 f ( x + y ) + ( a 2 - k b 2 ) a 2 f ( x ) where $$a\ne \pm 1, 0; b\ne \pm 1, 0; k>0$$ a ≠ ± 1 , 0 ; b ≠ ± 1 , 0 ; k > 0 in Banach space and Intuitionistic fuzzy normed spaces using both direct and fixed point methods.
The Journal of Analysis – Springer Journals
Published: Jun 8, 2018
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