A coefficient inequality for Bloch functions with applications to uniformly locally univalent functions

Abstract

We give a Fekete-Szegö type inequality for a Bloch function with Bloch seminorm ≤ 1. As an application of it, we derive a sharp coefficient inequality for a₃ for a uniformly locally univalent function f(z)=z+a₂z²+a₃z³+... on the unit disk with pre-Schwarzian norm ≤ λ for a given λ>0.

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