ABSTRACT
Let R be a prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, be a multilinear polynomial over C, which is not central valued on R. If d is a nonzero derivation of R and F is a generalized derivation of R such that
there exists a∈U such that F(x) = xa for all x∈R with a2∈C;
there exists a∈U such that F(x) = ax for all x∈R with a2∈C.
Acknowledgment
The authors would like to express their sincere thanks to referees for their valuable comments and suggestions which help to improve the quality of paper.