Differential Subordinations For Functions With Positive Real Part Using Admissibility Conditions

TL;DR

This paper establishes new sufficient conditions using admissibility criteria for differential subordinations involving functions with positive real part, leading to criteria for Janowski starlikeness.

Contribution

It introduces novel admissibility conditions for differential subordinations related to functions with positive real part, extending the theory to Janowski functions and their starlikeness.

Findings

Derived conditions for first, second, third order differential subordinations.

Established criteria for Janowski starlikeness.

Applied admissibility conditions to specific functions like exponential and sigmoid.

Abstract

Some sufficient conditions on certain constants which are involved in some first, second and third order differential subordinations associated with certain functions with positive real part like modified Sigmoid function, exponential function and Janowski function are obtained so that the analytic function p normalized by the condition p(0) = 1, is subordinate to Janowski function. The admissibility conditions for Janowski function are used as a tool in the proof of the results. As application, several sufficient conditions are also computed for Janowski starlikeness.