The Implementation of Differential Subordination and Superordination Theorems for Achieving Positive Analytic Functions

Abstract

Here observe that 2 1 q and q the most excellent subordinate and best leading. The applications are applied of those results are equivalent; et va p as well as like φ ln ≈ ≈ask as well as results to generalize and number of known results. By using a method based upon the Briot-Bouquet differential subordination, we prove several subordination results involving starlike and convex functions of complex order. Some special cases and consequences of the main subordination results are also indicated [I]. The main object of the present sequel to the aforementioned works is to apply a method based upon the Briot-Bouquet differential subordination in order to derive several subordination results involving starlike and convex functions of complex order[II], [III]. We also indicate some interesting special cases and consequences of our main subordination results.