# The Jacobian conjecture and injectivity conditions

## TL;DR

This paper introduces a class of polynomial mappings satisfying the Jacobian conjecture, proves several global univalence theorems, and discusses their applications, advancing understanding of polynomial injectivity.

## Contribution

It identifies specific polynomial mappings where the Jacobian conjecture holds and establishes new global univalence theorems with practical applications.

## Key findings

- Identified polynomial mappings satisfying the Jacobian conjecture
- Proved several global univalence theorems
- Presented applications of these theorems

## Abstract

One of the aims of this article is to provide a class of polynomial mappings for which the Jacobian conjecture is true. Also, we state and prove several global univalence theorems and present a couple of applications of them.