A Theory of Quaternionic G-Monogenic Mappings in \(E_{3}\)

  • T. S. Kuzmenko
  • V. S. ShpakivskyiEmail author
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 179)


We consider a class of so-called quaternionic G-monogenic (differentiable in the sense of Gâteaux) mappings and propose a description of all mappings in 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 one complex variable (the surface and the curvilinear Cauchy integral theorems, the Morera theorem), and Taylor and Laurent expansions. Moreover, we introduce a new class of quaternionic H-monogenic (differentiable in the sense of Hausdorff) mappings and establish the relation between G-monogenic and H-monogenic mappings. In addition, we prove the theorem of equivalence of different definitions of a G-monogenic mapping.


Algebra of complex quaternions G-monogenic mappings Constructive description Integral theorems Taylor and Laurent expansions Singular points H-monogenic mappings 



This research is partially supported by Grant of Ministry of Education and Science of Ukraine (Project No. 0116U001528).


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Authors and Affiliations

  1. 1.Department of Complex Analysis and Potential TheoryInstitute of Mathematics of the National Academy of Science of UkraineKyivUkraine

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