  Let $A$ be an algebra with a right identity. In this paper, we study $(p,
q)-$centralizers of $A$ and show that every $(p, q)-$centralizer of $A$ is a
two-sided centralizer. In the case where, $A$ is normed algebra, we also prove
that $(p, q)-$centralizers of $A$ are bounded. Then, we apply the results for
some group algebras and verify that $L^1(G)$ has a nonzero weakly compact $(p,
q)-$centralizer if and only if $G$ is compact and the center of $L^1(G)$ is
non-zero. Finally, we investigate $(p, q)-$Jordan centralizers of $A$ and
determine them.
