Jordan superderivations and generalized Jordan superderivations of generalized matrix algebras

Let [Formula: see text] be a generalized matrix algebra defined by the Morita context. We consider [Formula: see text] as a superalgebra following the method proposed by Ghahramani and Heidari Zadeh. This paper investigates the problem of describing the form of Jordan superderivations on generalized matrix algebras. It turns out that in generalized matrix algebras, there exist Jordan superderivations that are not superderivations. Additionally, we show that every generalized Jordan superderivation on a class of generalized matrix algebras can be expressed as the sum of a generalized superderivation and an anti-superderivation. Consequently, we characterize (generalized) Jordan superderivation on a triangular algebra. In particular, we deduce that any (generalized) Jordan superderivation of an upper triangular algebra, under certain conditions, is a (generalized) derivation.