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

N-multipliers and their relations with n-homomorphisms