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 this paper, a generalized derivatives operator n
λ,βf
introduced by the authors will be discussed. Some subordination and
superordination results involving this operator for certain normalized
analytic functions in the open unit disk will be investigated. Our
results extend corresponding previously known results.
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.