On Bohr and Bohr-Rogosinski phenomena for subclasses of univalent functions

Abstract

In this paper, we establish sharp Bohr and Bohr–Rogosinski-type inequalities for several sub-classes of univalent functions in the unit disk, including starlike, convex, odd, and even functions, as well as Mocanu’s class of analytic functions. Using refined coefficient estimates and growth bounds, we determine exact Bohr and Rogosinski radii for each class, with sharpness verified through extremal examples such as the Koebe function and its variants. We also derive the Bohr radii for the convolution analogues of univalent and convex functions. Our results refine and extend existing inequalities, provide new radii for symmetric subclasses, and contribute to a deeper understanding of the Bohr phenomenon in geometric function theory.