Abstract: the present paper, using the technique of differential subordination, we obtain certain results for analytic functions defined by a multiplier transformation in the open unit disc E = { z : IzI < 1}. We claim that our results extend and generalize the existing results in this particular direction
Abstract: In the present paper, we investigate a differential subordination
involving multiplier transformation related to a sector in the
open unit disk E = {z : |z| < 1}. As special cases to our main
result, certain sufficient conditions for strongly starlike and strongly
convex functions are obtained.
Abstract: In the present paper, we obtain a sandwich-type theorem.
As applications of our main result, we discuss the univalence
and starlikeness of analytic functions in terms of certain differential
subordinations and differential inequalities.