Abstract
Let be a ring containing a nontrivial idempotent with the center Z(
) and ℕ be the set of all non-negative integers. Let Δ = {Gn}n∈ℕ be a family of mappings Gn :
(not necessarily additive) such that
, the identity mapping of
. Then Δ is said to be a generalized Lie triple higher derivable mapping of
holds for all a; b; c ∈
and for each n ∈ ℕ, where
is a family of mappings
(not necessarily additive) such that
satisfying
for each n ∈ ℕ, a, b, c ∈
. In the present paper, it is shown that, if
is a ring containing a nontrivial idempotent which admits a generalized Lie triple higher derivable mapping Δ = {Gn}n∈ℕ, then there exists an element za,b (depending on a and b) in the center Z(
) such that Gn(a + b) = Gn(a)+ Gn(b)+ za,b for all a, b ∈
and for each n ∈ ℕ.