Generalized Derivations on Prime Near Rings

Let N be a near ring. An additive mapping f:N→N is said to be aright generalized (resp., left generalized) derivation with associated derivation d on N if f(xy)=f(x)y+xd(y) (resp., f(xy)=d(x)y+xf(y)) for all x,y∈N. A mappingf:N→N is said to be a generalized derivation with associated derivation d on N iff is both a right generalized and a left generalized derivation with associated derivationd on N. The purpose of the present paper is to prove some theorems in the setting ofa semigroup ideal of a 3-prime near ring admitting a generalized derivation, therebyextending some known results on derivations