# Stability of a Quadratic Functional Equation Originating From Sum of the Medians of a Triangle in Fuzzy Ternary Banach Algebras: Direct and Fixed Point Methods

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## Keywords:

Fuzzy ternary Banach algebra, Quadratic functional equation, Ulam - Hyers stability, Fixed point method## Abstract

In this paper, we obtain the solution in vector space and the generalized Ulam-Hyers stability of the ternary quadratic homomorphisms and ternary quadratic derivations between fuzzy ternary Banach algebras associated to the quadratic functional equation

\begin{align*}

f\left(\frac{x+y}{2}-z\right)+f\left(\frac{y+z}{2}-x\right)+f\left(\frac{z+x}{2}-y\right)=\frac{3}{4}\left(f(x-y)+f(y-z)+f(z-x)\right)

\end{align*}

originating from sum of the medians of a triangle by using direct and fixed point methods. An application of this functional equation is also studied.

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*International Journal of Mathematics And Its Applications*,

*3*(4 - A), 45–64. Retrieved from https://ijmaa.in/index.php/ijmaa/article/view/485

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