Quaternionic G -Monogenic Mappings in E m

We consider a class of so-called quaternionic G-monogenic mappings associated with m-dimensional (m 2 f2; 3; 4g) partial differential equations and propose a description of all mappings from this class by using four analytic functions of complex variable. For G-monogenic mappings we generalize some analogues of classical integral theorems of the holomorphic function theory of the complex variable (the surface and the curvilinear Cauchy integral theorems, the Cauchy integral formula, the Morera theorem), and Taylor’s and Laurent’s expansions. Moreover, we investigated the relation between G-monogenic and H-monogenic (differentiable in the sense of Hausdorff) quaternionic mappings.