Let R be ring, and d:R R is aditif mapping then
d is called derivation if
d(ab)=d(a)b+ad(b) a,b R
d is called Jordan derivation if
d(a^2)=d(a)a+ad(a) a R
Obviously any derivation is Jordan derivation.
But the converse is not true. (is there any example to show this statement?)