Shpakivskyi, V. S. and Kuzmenko, T. S.
(2018)
Quaternionic G–Monogenic Mappings in Em.
International Journal of Advanced Research in Mathematics, 12.
pp. 134.
ISSN 22976213
Abstract
We consider a class of socalled quaternionic Gmonogenic mappings associated with mdimensional (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 Gmonogenic 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 Gmonogenic and Hmonogenic (differentiable in the sense of Hausdorff) quaternionic
mappings.
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