Abstract
In this paper, we aim to present a survey on subordination and superordination theorems related to the class of analytic functions defined in a symmetric domain, which is the open unit disc. The results were deduced by making use of a new differential operator. We present two properties of this operator from which we constructed the final results. Moreover, based on the obtained outcomes, we give two sandwich-type theorems. Some interesting further consequences are also taken into consideration.
Highlights
Introduction and DefinitionsLet us denote by H the set of analytic functions defined in the open unit disc U ={z ∈ C : |z| < 1}
We proposed a new form of a differential operator I m,β (λ, l ), which generalizes several operators introduced earlier by many other researchers
Using the method of admissible function, we deduced certain differential subordination results associated with two properties of the newly introduced operator
Summary
Introduction and DefinitionsLet us denote by H the set of analytic functions defined in the open unit disc U ={z ∈ C : |z| < 1}. Let us denote by H the set of analytic functions defined in the open unit disc U = If we consider two univalent functions p and φ( p(z), zp0 (z), z2 p00 (z); z) and if the function p verifies the second order differential superordination creativecommons.org/licenses/by/
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