Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47886120200101On Pair of Generalized Derivations in Rings87949717410.22034/kjm.2019.97174ENAsmaAliDepartment of Mathematics, Aligarh Muslim University, Aligarh-202002,
India.Md HamidurRahamanDepartment of Mathematics, Aligarh Muslim University, Aligarh-202002,
India.Journal Article20181212Let $R$ be an associative ring with extended centroid $C$, let $G$ and $F$ be generalized derivations of $R$ associated with nonzero derivations $\delta$ and $d$, respectively, and let $m, k, n \geq1$ be fixed integers. In the present paper, we study the situations: (i)$F(x)\circ_{m}G(y)=(x \circ_{n} y)^{k}$, (ii) $[F(x),y]_{m}+[x,d(y)]_{n}=0$ for all $y, x$ in some appropriate subset of $R$.http://www.kjm-math.org/article_97174_d6600441ebda02c760dafc2171b8c9a6.pdf