Curvilinear integral theorem for $G$-monogenic mappings in the algebra of complex quaternion

TL;DR

This paper extends the classical Cauchy integral theorem to $G$-monogenic mappings in complex quaternion algebra, specifically for boundary curves, providing a new integral formula in this algebraic setting.

Contribution

It introduces a curvilinear integral theorem for $G$-monogenic mappings on the boundary of a domain in complex quaternion algebra, expanding the scope of quaternionic analysis.

Findings

Established a boundary version of the Cauchy integral theorem for $G$-monogenic functions.

Derived an integral formula applicable to boundary curves in complex quaternion algebra.

Extended classical complex analysis results to quaternionic function theory.

Abstract

For $G$-monogenic mappings taking values in the algebra of complex quaternion we prove a curvilinear analogue of the Cauchy integral theorem in the case where a curve of integration lies on the boundary of a domain.