Approximate Generalized Derivations On Triangular Banach Algebras Associated to Modules

Abstract

‎In this paper‎, ‎we introduce the concept of approximate generalized derivation on modules‎. ‎In the following‎, ‎we investigate the approximate generalized derivations on triangular Banach algebras associated with modules and for Banach algebra $A$‎, ‎we show that there is a relationship between approximate generalized derivations on Banach right $A$-module $X$ and approximate generalized derivations on triangular Banach algebra $\mathcal{T}=\left[‎ ‎\begin{array}{rr}‎ ‎\mathcal{B}(X) & X \\‎ ‎& A‎ ‎\end{array} \right]$‎.