Bohr phenomenon for analytic functions subordinate to starlike or convex functions

Abstract

In this paper, we will obtain a new result on the Bohr phenomenon for analytic functions f which are subordinate to starlike functions g∈S⁎(ϕ), where ϕ satisfies Ma-Minda conditions and the coefficients of ϕ are non-negative. Next, we will obtain a new result on the Bohr phenomenon for analytic functions f which are subordinate to convex functions g∈C(ϕ), where ϕ satisfies Ma-Minda conditions. In this result, we obtain that the Bohr radius r˜ϕ satisfies r˜ϕ≥1/3 by using a new idea. Finally, we will give the Bohr phenomenon for starlike functions with respect to a boundary point.