Abstract
In this paper, we introduce ternary quadratic Pompeiu functional equations in ternary Banach algebras. Moreover, we investigate the general solution and the generalized Hyers–Ulam stability of ternary quadratic Pompeiu functional equation and other type of this new equation $$\begin{aligned}&f(x+y+z+[xyz])+f(x+y+z-[xyz])+2f(x)+2f(y)+2f(z)\\&\quad =2f(x+y)+2f(y+z)+2f(x+z)+2[f(x)f(y)f(z)]. \end{aligned}$$
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