# Differential Subordination for Janowski Functions with Positive Real Part

## TL;DR

This paper uses differential subordination theory to establish new sufficient conditions for functions to be Janowski functions with positive real part, aiding in identifying Janowski starlike functions.

## Contribution

It applies first order differential subordination to derive novel criteria for Janowski functions with positive real part, expanding the theoretical framework.

## Key findings

- Derived new sufficient conditions for Janowski functions
- Established criteria for Janowski starlike functions
- Enhanced understanding of differential subordination applications

## Abstract

Theory of differential subordination provides techniques to reduce differential subordination problems into verifying some simple algebraic condition called admissibility condition. We exploit the first order differential subordination theory to get several sufficient conditions for function satisfying several differential subordinations to be a Janowski function with positive real part. As applications, we obtain sufficient conditions for normalized analytic functions to be Janowski starlike functions.