Sufficient conditions for starlikeness and convexity

In this paper, the differential subordination \( \frac{b}{\phi(z)}+ c~ \phi(z) + d~ \frac{z \phi'(z)}{\phi^{k}(z)} \prec s(z), k\geq 1, z\in\mathbb{E}\) is studied by using Lowner Chain. The corresponding result for differential superordination is also obtained to get sandwich type result. Consequently, we obtain sufficient conditions for Starlikeness and Convexity of analytic function \(f\).