Let denote the class of analytic functions in the unit disk and let the integral operator , be defined by
If and is univalent in we say that is subordinate to or is superordinate to , written , if and . In a recent paper S. S. Miller and P. T. Mocanu have determined conditions on such that
for all functions that satisfy the above superordination. In this paper the author determines sufficient conditions on and such that the following differential superordination holds:
The function is the largest function so that the right-hand side holds, for all functions satisfying the left-hand side differential super-ordination. The particular case is considered.