Let
$G$
be a group and
$\mathbb{K}\,=\,\mathbb{C}\,\text{or}\,\mathbb{R}$
. In this article, as a generalization of the result of Albert and Baker, we investigate the behavior of bounded and unbounded functions
$f\,:\,G\,\to \,\mathbb{K}$
satisfying the inequality
$$\left| f\left( \sum\limits_{k=1}^{n}{{{x}_{k}}} \right)\,-\,\underset{k=1}{\overset{n}{\mathop{\Pi }}}\,f\left( {{x}_{k}} \right) \right|\,\,\le \phi \left( {{x}_{2}},\,.\,.\,.\,,{{x}_{n}} \right),\,\,\,\,\,\,\forall {{x}_{1}},\,.\,.\,.\,,{{x}_{n}}\,\in \,G,$$
Where
$\phi :\,{{G}^{n-1}}\,\to \,[0,\,\infty )$
. Also as a a distributional version of the above inequality we consider the stability of the functional equation
$$u\,\circ \,S\,-\,\overbrace{u\,\otimes \,.\,.\,.\,\otimes \,u}^{n-\text{times}}\,=\,0,$$
where
$u$
is a Schwartz distribution or Gelfand hyperfunction,
$\circ$
and
$\otimes$
are the pullback and tensor product of distributions, respectively, and
$S\left( {{x}_{1}},\,.\,.\,.\,,{{x}_{n}} \right)\,=\,{{x}_{1}}\,+\,.\,.\,.\,+\,{{x}_{n}}$
.