On monogenic mappings of the quaternionic variables

TL;DR

This paper introduces a new class of quaternionic mappings called $H$-monogenic, explores their relation to existing $G$-monogenic mappings, and proves the equivalence of different definitions of $G$-monogenic mappings.

Contribution

It extends the theory of quaternionic differentiability by defining $H$-monogenic mappings and establishing their relation to $G$-monogenic mappings, including equivalence of definitions.

Findings

Introduction of quaternionic $H$-monogenic mappings

Relation established between $G$-monogenic and $H$-monogenic mappings

Proof of equivalence of different $G$-monogenic definitions

Abstract

In the paper [1] we consider a new class, so-called, $G$-monogenic (differentiable in the sense of Gateaux) quaternionic mappings. In the present paper we introduce quaternionic $H$-monogenic (differentiable in the sense of Hausdorff) mappings and establish the relation between $G$-monogenic and $H$-monogenic mappings. The equivalence of different definitions of $G$-monogenic mapping is proved.