@article{Hermas_Oukhtite_Taoufiq_2023, title={Generalized derivations acting on Lie ideals in prime rings and Banach algebras}, volume={60}, url={http://www.matstud.org.ua/ojs/index.php/matstud/article/view/394}, DOI={10.30970/ms.60.1.3-11}, abstractNote={<p>Let $R$ be a prime ring and $L$ a non-central Lie ideal of $R.$ The purpose of this paper is to describe generalized derivations of $R$ satisfying some algebraic identities locally on $L.$ More precisely, we consider two generalized derivations $F_1$ and $F_2$ of a prime ring $R$ satisfying one of the following identities:<br>1. $F_1(x)\circ y +x \circ F_2(y) =0,$<br>2. $[F_1(x),y] + F_2([x,y]) =0,$<br>for all $x,y$ in a non-central Lie ideal $L$ of $R.$ Furthermore, as an application, we study continuous generalized derivations satisfying similar algebraic identities with power values on nonvoid<br>open subsets of a prime Banach algebra $A$. Our topological approach is based on Baire’s<br>category theorem and some properties from functional analysis.</p>}, number={1}, journal={Matematychni Studii}, author={Hermas, A. and Oukhtite, L. and Taoufiq, L.}, year={2023}, month={Sep.}, pages={3-11} }