Generalized distance-squared mappings of the plane into the plane

TL;DR

This paper introduces and classifies generalized distance-squared mappings from the plane to the plane, providing a systematic understanding of their structure and properties.

Contribution

It defines a new class of mappings called generalized distance-squared mappings and classifies them specifically for the plane-to-plane case.

Findings

Complete classification of plane-to-plane generalized distance-squared mappings

Recognition criteria for these mappings

Structural insights into their geometric properties

Abstract

We define generalized distance-squared mappings, and we concentrate on the plane to plane case. We classify generalized distance-squared mappings of the plane into the plane in a recognizable way.