On monogenic mappings of a quaternionic variable

Abstract

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