Subordinations of the solutions of Briot–Bouquet differential equations and their applications

Abstract

In this paper, we give some sufficient and necessary conditions for subordination of the solution of the Briot–Bouquet differential equation: where δ and λ are real numbers with δ≠0, δ+λ>0, and U is the unit disc in the complex plane C. Using these subordinations, we obtain some sufficient and necessary conditions that the integral operators and preserve starlikeness, where α, β, δ, and γ are real numbers with α+δ=β+γ>0, αβ≠0.