On Bloch's Theorem and the contraction mapping principle

TL;DR

This paper presents new proofs of Bloch's theorem and a Bloch-type theorem for Wu K-mappings using Banach's contraction mapping principle, offering a novel approach to classical results in complex analysis.

Contribution

It introduces a new proof technique based on contraction mappings for Bloch's theorem and extends it to Wu K-mappings, providing fresh insights and methods.

Findings

New proof of Bloch's theorem using contraction mapping

Extension of Bloch-type theorem to Wu K-mappings

Demonstrates the versatility of Banach's contraction principle in complex analysis

Abstract

In this paper we give a new proof, relying on Banach's contraction mapping principle, of a celebrated theorem of Andr\'e Bloch. Also, via the same contraction mapping principle, we give a proof of a Bloch type theorem for normalised Wu $K$-mappings.