%0 Journal Article
%@ 2297-6213
%A Shpakivskyi, V. S.
%A Kuzmenko, T. S.
%D 2018
%F zu2:28514
%I SciPress Ltd., Switzerland
%J International Journal of Advanced Research in Mathematics
%K complex quaternions algebra, Gâteaux derivative, G-monogenic mappings, constructive  description, integral theorems, Taylor’s and Laurent’s expansions, singular points, H-monogenic  mappings.
%P 1-34
%T Quaternionic G–Monogenic Mappings in Em
%U http://eprints.zu.edu.ua/28514/
%V 12
%X 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.