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, the authors established the solution of the additive functional equation and inequality$$f(x)+f(y+z)-f(x+y)=f(z)$$and$$\|f(x)+f(y+z)-f(x+y)\| \leq\|f(z)\| .$$We also prove that the above functional equation and inequality are stable in Banach space in the sense of Ulam, Hyers, Rassias. An application of this functional equation is also studied.

In this paper, the authors introduced and investigated the general solution of system of quartic functional equations$$\begin{aligned}& f(x+y+z)+f(x+y-z)+f(x-y+z)+f(x-y-z) \\& =2[f(x+y)+f(x-y)+f(x+z)+f(x-z)+f(y+z)+f(y-z)] \\& -4[f(x)+f(y)+f(z)] \\& f(3 x+2 y+z)+f(3 x+2 y-z)+f(3 x-2 y+z)+f(3 x-2 y-z) \\& =72[f(x+y)+f(x-y)]+18[f(x+z)+f(x-z)]+8[f(y+z)+f(y-z)] \\& +144 f(x)-96 f(y)-48 f(z) \\& f(x+2 y+3 z)+f(x+2 y-3 z)+f(x-2 y+3 z)+f(x-2 y-3 z) \\& =8[f(x+y)+f(x-y)]+18[f(x+z)+f(x-z)]+72[f(y+z)+f(y-z)] \\& -48 f(x)-96 f(y)+144 f(z) \text {. } \\&\end{aligned}$$Its generalized Hyers-Ulam stability using Hyers direct method and fixed point method are discussed. Counter examples for non stable cases are also given.

The main goal of this paper is to found the generalized Ulam-Hyers stability of a radical reciprocal quadratic functional equation originating from 3 dimensional Pythagorean means in Fuzzy Banach space using classical Hyers method.

In this paper, the authors obtain the general solution and generalized Ulam - Hyers stability of an (AQQ): additive - quadratic - quartic functional equation of the form$$\begin{aligned}f(x+y+z) & +f(x+y-z)+f(x-y+z)+f(x-y-z) \\=2[f(x+y) & +f(x-y)+f(y+z)+f(y-z)+f(x+z)+f(x-z)] \\& -4 f(x)-4 f(y)-2[f(z)+f(-z)]\end{aligned}$$by using the classical Hyers' direct method. Counter examples for non stability are discussed also.