Abstract
In this paper, we acquire the general solution of the generalized quadratic functional equation $ \begin{aligned} \sum\limits_{1 \leq a \lt b \lt c \leq m}\varphi\left(r_{a}+r_{b}+r_{c}\right)& = (m-2)\sum\limits_{1\leq a \lt b\leq m}\varphi\left(r_{a}+r_{b}\right) &\quad-\left(\frac{m^{2}-3m+2}{2}\right)\nonumber \sum\limits_{a = 1}^{m}\frac{\varphi\left(r_{a}\right)+\varphi\left(-r_{a}\right)}{2} \end{aligned} $ where $m\geqslant 3$ is an integer. We also investigate Hyers-Ulam stability results by means of using alternative fixed point theorem for this generalized quadratic functional equation.
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