TY - JOUR
T1 - Quaternionic G-Monogenic Mappings in Em
AU - Shpakivskyi, Vitalii S.
AU - Kuzmenko, Tetyana S.
JF - International Journal of Advanced Research in Mathematics
VL - 12
SP - 1
EP - 34
SN - 2297-6213
PY - 2018
PB - SciPress Ltd
DO - 10.18052/www.scipress.com/IJARM.12.1
UR - https://www.scipress.com/IJARM.12.1
KW - Complex Quaternions Algebra
KW - Constructive Description
KW - Gateaux Derivative
KW - G-Monogenic Mappings
KW - H-Monogenic Mappings
KW - Integral Theorems
KW - Singular Points
KW - Taylor’s and Laurent’s Expansions
AB - We consider a class of so-called quaternionic G-monogenic mappings associatedwith m-dimensional (m 2 f2; 3; 4g) partial differential equations and propose a description of allmappings from this class by using four analytic functions of complex variable. For G-monogenicmappings we generalize some analogues of classical integral theorems of the holomorphic functiontheory 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 (differentiablein the sense of Hausdorff) quaternionic mappings.
ER -