The main purpose of this research is to characterize generalized (left) derivations and Jordan (*,*)-derivations on Banach algebras rings using some functional identities. Let A be a unital semiprime algebra let F,G : ? linear mappings satisfying F(x) =-x2G(x-1) for all x Inv(A), where Inv(A) denotes the set invertible elements A. Then both F G are Another result in regard as follows. n > 1 ...

In this paper, we consider Leibniz algebras with derivations. A pair consisting of a algebra and distinguished derivation is called LeibDer pair. We define cohomology theory for coefficients in representation. study central extensions the next, generalize formal deformation to pairs which deform both bracket derivation. It governed by itself. Finally, homotopy derivations on sh 2-derivations 2-...

 Motivated by the intensive and powerful works concerning additive‎ ‎mappings of operator algebras‎, ‎we mainly study Lie-type higher‎ ‎derivations on operator algebras in the current work‎. ‎It is shown‎ ‎that every Lie (triple-)higher derivation on some classical operator‎ ‎algebras is of standard form‎. ‎The definition of Lie $n$-higher‎ ‎derivations on operator algebras and related pot...