Bohr radius for the punctured disk

Abstract

This paper investigates the Bohr phenomenon for the class of analytic functions from the unit disk into the punctured unit disk. The Bohr radius is shown to be 1/3.

Some Bohr-Type Inequalities for Bounded Analytic Functions

“…Hu et al [8,9] established some Bohr inequalities with one parameter or involving convex combination. Abu-Muhanna [10] investigated the Bohr phenomenon for the class of analytic functions from the unit disk into the punctured unit disk. Some authors considered the Bohr phenomenon for functions defined on other domains, such as concave-wedge domain [11,12], convex domain [13], and the exterior of a compact domain [14].…”