^{1}Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Iran;

^{2}Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Iran

Abstract

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