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

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Models and Theories in Social Systems

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 179))

Abstract

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.

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Acknowledgements

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. Department of Complex Analysis and Potential Theory, Institute of Mathematics of the National Academy of Science of Ukraine, 3, Tereshchenkivs’ka st., Kyiv, 01004, Ukraine

    T. S. Kuzmenko & V. S. Shpakivskyi

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  1. T. S. Kuzmenko
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  2. V. S. Shpakivskyi
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Correspondence to V. S. Shpakivskyi .

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Editors and Affiliations

  1. Faculty of Mathematics and Computer Science, Ovidius University of ConstanĹŁa, ConstanĹŁa, Romania

    Cristina Flaut

  2. Department of Mathematics and Physics, Faculty of Military Technology, University of Defence, Brno, Czech Republic

    Šárka Hošková-Mayerová

  3. Faculty of History and Political Science, Ovidius University of ConstanĹŁa, ConstanĹŁa, Romania

    Daniel Flaut

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Kuzmenko, T.S., Shpakivskyi, V.S. (2019). A Theory of Quaternionic G-Monogenic Mappings in \(E_{3}\). In: Flaut, C., Hošková-Mayerová, Š., Flaut, D. (eds) Models and Theories in Social Systems. Studies in Systems, Decision and Control, vol 179. Springer, Cham. https://doi.org/10.1007/978-3-030-00084-4_25

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