  Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule. We introduce
and study the notions of $n$-multipliers and approximate local $n$-multipliers
by generalizing the classical concept of multipliers from $A$ into $X$. As an
algebraic result, we construct a Banach algebra consisting of $n$-multipliers
on $A$ and under some mild conditions, we give a nice relation of this algebra
with $n$-homomorphisms from $A$ into $\mathbb{C}$.
