Differential Subordination and superordination Results Associated with Generalized Derivative operator

Abstract

Using the methods of differential subordination and superordination, sufficient conditions are determined on the generalized derivative operator for analytic functions in the open unit disc U to obtain, these results are obtained by investigating appropriate classes of admissible functions. New differential sandwich-type results are also obtained for the generalized derivative. Some of the results established in this paper would provide extensions of those given in earlier works.