A first-order differential double subordination with applications

TL;DR

This paper establishes sufficient conditions for normalized analytic functions to satisfy a double subordination chain using differential inequalities, with applications to univalent and a-like functions.

Contribution

It introduces a novel differential sandwich-type result for double subordination involving normalized analytic functions.

Findings

Derived sufficient conditions for double subordination chains.

Applied results to univalent functions.

Extended applications to a-like functions.

Abstract

Let $q_1$ and $q_2$ belong to a certain class of normalized analytic univalent functions in the open unit disk of the complex plane. Sufficient conditions are obtained for normalized analytic functions $p$ to satisfy the double subordination chain $q_1(z)\prec p(z)\prec q_2(z)$. The differential sandwich-type result obtained is applied to normalized univalent functions and to $\Phi$-like functions.