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On monogenic mappings of a quaternionic variable

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Abstract

Earlier [1], a new class of quaternionic so-called G-monogenic (differentiable in the meaning of Gâteaux) mappings was considered. In the present paper, we introduce quaternionic H-monogenic (differentiable in the sense of Hausdorff) mappings and establish a relation between G- and H-monogenic mappings. The equivalence of different definitions of a G-monogenic mapping is proved.

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Authors and Affiliations

  1. Institute of Mathematics of the NAS of Ukraine, Kiev, Ukraine

    Vitalii S. Shpakivskyi

  2. Institute of Mathematics of the NAS of Ukraine, Kiev, Ukraine

    Tat’yana S. Kuzmenko

Authors
  1. Vitalii S. Shpakivskyi
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  2. Tat’yana S. Kuzmenko
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Corresponding author

Correspondence to Vitalii S. Shpakivskyi.

Additional information

Presented by V. Ya. Gutlyanskiĭ

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 13, No. 2, pp. 270–289 April–June, 2016.

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

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Shpakivskyi, V.S., Kuzmenko, T.S. On monogenic mappings of a quaternionic variable. J Math Sci 221, 712–726 (2017). https://doi.org/10.1007/s10958-017-3260-4

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  • DOI: https://doi.org/10.1007/s10958-017-3260-4

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