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.

In this paper, the authors investigated the general solution and generalized Ulam - Hyers stability of $a_i$ type $n$ - variable multi $n$ - dimensional additive functional equation$$\begin{aligned}2 h\left(\sum_{i=1}^n a_i x_{1 i}\right. & \left., \sum_{i=1}^n a_i x_{2 i}, \ldots \ldots, \sum_{i=1}^n a_i x_{n i}\right) \\= & \left(\sum_{i=1}^n a_i\right) h\left(\sum_{i=1}^n x_{1 i}, \sum_{i=1}^n x_{2 i}, \ldots \ldots, \sum_{i=1}^n x_{n i}\right) \\& +\left(a_1-\sum_{i=2}^n a_i\right) h\left(x_{11}-\sum_{i=2}^n x_{1 i}, x_{21}-\sum_{i=2}^n x_{2 i}, \ldots \ldots, x_{n 1}-\sum_{i=2}^n x_{n i}\right)\end{aligned}$$where $a_i(i=1,2, \ldots n)$ are different integers greater than 1 , using two different technique.

In this paper, we achieve the general solution and generalized Ulam - Hyers stability of a $n$-dimensional additive-quadratic-cubic-quartic (AQCQ) functional equation$$\begin{aligned}f\left(\sum_{i=1}^{n-1} v_i+2 v_n\right)+f\left(\sum_{i=1}^{n-1} v_i-2 v_n\right)= & 4 f\left(\sum_{i=1}^n v_i\right)+4 f\left(\sum_{i=1}^{n-1} v_i-v_n\right)-6 f\left(\sum_{i=1}^{n-1} v_i\right) \\& +f\left(2 v_n\right)+f\left(-2 v_n\right)-4 f\left(v_n\right)-4 f\left(-v_n\right)\end{aligned}$$where $n$ is a positive integer with $n \geq 3$ in Banach Space (BS) via direct and fixed point methods. The stability results are discussed in two different ways by assuming $n$ is an odd positive integer and $n$ is an even positive integer.

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