In this paper, authors verify the generalized Ulam -Hyers stability of the following Euler -Lagrange additive functional equationin Intuitionistic Fuzzy Banach Spaces using direct and fixed point methods.

In this paper, we obtain the generalized Ulam - Hyers stability of a 2 - variable AC - mixed type functional equation$$f(2 x+y, 2 z+w)-f(2 x-y, 2 z-w)=4[f(x+y, z+w)-f(x-y, z-w)]-6 f(y, w)$$in Quasi - Beta normed space using direct and fixed point methods.

In this paper, we introduce and investigate the general solution and generalized Ulam- Hyers stability of a additive functional equation$$f\left(\frac{\sum_{k=1}^N x_k}{N}\right)=\frac{1}{N} \sum_{k=1}^N f\left(x_k\right)$$originating from $N$ observations of an arithmetic mean in Banach spaces using various substitutions in two different approaches with $N \geq 2$.