Abstract
Let n >= 1 be a fixed integer and R be an (n + 1)! -torsion free ring. If
F, d : R-m -> R are two permuting m-additive mappings satisfying
F(x(1), ..., x(i-1), x(i)(n+1), x(i+1), ..., x(m))
= F(x(1), ..., x(i-1), x(i), x(i+1), ..., x(m))x(i)(n)
+ Sigma(n)(j=1) x(i)(j) d(x(1), ..., x(i-1), x(i), x(i+1), ..., x(m))x(i)(n - j)
for all x(i) is an element of R and for all i = 1, 2, ..., m, then d is a Jordan m-derivation and F is a generalized Jordan m-derivation on R.