Some applications of differential subordination for certain starlike functions

TL;DR

This paper explores the properties of a specific class of starlike functions defined by a differential inequality, establishing subordination relations and deriving related corollaries for subclasses of analytic functions.

Contribution

It introduces new subordination relations for the class al S^*(q_c) of starlike functions and applies these to obtain results for related subclasses.

Findings

Established subordination relations for al S^*(q_c)

Derived corollaries for subclasses of analytic functions

Enhanced understanding of starlike functions with differential inequalities

Abstract

We consider the class $\mathcal{S}^*(q_c)$ of normalized starlike functions $f$ analytic in the open unit disk $|z|<1$ that satisfying the inequality \begin{equation*} \left|\left(\frac{zf'(z)}{f(z)}\right)^2-1\right|<c \quad (0<c\leq1). \end{equation*} In this article, we present some subordination relations and these relations are then used to obtain some corollaries for some subclass of analytic functions.