Expansion of implicit mapping theory to split-quaternionic maps in Clifford analysis

Abstract

This paper presents the regularity of a split-quaternionic function and a corresponding split-Cauchy–Riemann system of a split quaternion. The properties of an inverse and an implicit mapping theory for a split-quaternionic map are investigated. In addition, the paper proposes a definition and expression for a split biregular mapping in an open set in $\mathbb{C}^2$. The obtained results are illustrated with some examples.