VARIOUS STABILITIES OF A GENERALIZED RECIPROCAL-QUADRATIC FUNCTIONAL EQUATION IN SEVERAL VARIABLES

Abstract

This study is aimed to determine various stabilities of a generalized reciprocal-quadratic functional equation of the form

\begin{equation*}
r\left(\sum_{j=1}^{p}\beta_ju_j\right)=\frac{\prod_{j=1}^{p}r\left(u_j\right)}{\left[\sum_{j=1}^{p}\beta_j\prod_{k=1,k\neq j}^{p}\sqrt{r\left(u_k\right)}\right]^2}
\end{equation*}

connected with Ulam, Hyers, Th.M. Rassias, J.M. Rassias and Gavruta in non-Archimedean fields, where $\beta_j; j=1,2,\dots,p$ are arbitrary and fixed real real numbers such that $\left(\beta_1,\beta_2,\dots,\beta_p\right)\neq (0,0,\dots,0)$ and $0<\beta_1+\beta_2+\dots+\beta_p=\sum_{j=1}^{p}\beta_j\neq 1$.