THE IMPLEMENTATION OF DIFFERENTIAL SUBORDINATION AND SUPERORDINATION THEOREMS FOR ACHIEVING POSITIVE ANALYTIC FUNCTIONS

DOI NO:

https://doi.org/10.26782/jmcms.2020.03.00004

Keywords:

convex function,Star like function function,Differential subordination,Differential super ordination,

Abstract

Suppose  assume that complex numbers  such thatas  well as well as  Where The conditions are satisfactory for analytic function Cauchy’s Riemann equations are satisfied for the functions Here observe that the most excellent  subordinate and best leading. The applications are applied of those results are equivalent;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.

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