# Stability of Generalized Quartic Functional Equation in Random Normed Spaces

## DOI:

https://doi.org/10.26713/cma.v14i5.2227## Keywords:

Quartic functional equation, Hyers- Ulam stability, Random normed space## Abstract

Aim of this paper is to investigate the Hyers-Ulam stability of generalized quartic functional equation

\begin{align*}

\sum^n_{i=1}\emptyset \bigg(-v_i+\sum^n_{j=1,i\neq j}{v_j}\bigg)

&=(n-8)\sum_{1=i<j<k<l=n}{\emptyset (v_i+v_j+v_k+v_l)}\nonumber\\&\quad -(n^2-12n+28)\sum_{1=i<j<k=n}{\emptyset (v_i+v_j+v_k)}\\

&\quad +\bigg(\frac{n^3-15n^2+60n-68}{2}\bigg)\sum_{1=i<j=n}{\emptyset (v_i+v_j)}\nonumber\\&\quad +2\sum_{1=i<j=n}{\emptyset (v_i-v_j)}+\sum^n_{i=1}{\emptyset}(3v_i)\\

&\quad-\bigg(\frac{{n^4-17n}^3+86n^2-148n+558}{6}\bigg)\sum^n_{i=1}{\emptyset (v_i)}

\end{align*}

in random normed space.

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*Communications in Mathematics and Applications*,

*14*(5), 1645–1651. https://doi.org/10.26713/cma.v14i5.2227

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