On Landau’s Type Estimates for Coefficients of Univalent Functions

Abstract

© 2020, Springer-Verlag GmbH Germany, part of Springer Nature. In this article we estimate the sum of coefficients for functions with restrictions on the pre-Schwarzian derivative. We obtain an estimate, which is sharp up to a constant and find upper and lower bounds for that constant. Also we estimate the sum of the first three coefficients for all functions f, such that log f′(z) is bounded with respect to the Bloch norm.