Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Iran


Let $R$ be a prime ring with extended centroid $C$, $H$ a generalized derivation of $R$ and $n\geq 1$ a fi xed integer. In this paper we study the situations: (1) If $(H(xy))^n =(H(x))^n(H(y))^n$ for all $x,y\in R$; (2) obtain some related result in case $R$ is a noncommutative Banach algebra and $H$ is continuous or spectrally bounded.


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