Open AccessON h-HOLOMORPHY AND h-ANALYTICITY OF FUNCTIONS OF AN h-COMPLEX VARIABLE
Author(s) -
V. A. Pavlovsky,
Igor L. Vasiliev
Publication year - 2020
Publication title -
l.n. gumilev atyndaġy euraziâ u̇lttyk̦ universitetìnìn̦ habaršysy. matematika, informatika, mehanika seriâsy
Language(s) - English
Resource type - Journals
eISSN - 2663-1326
pISSN - 2616-7182
DOI - 10.32523/2616-7182/2020-133-4-19-27
Subject(s) - uniqueness , mathematics , differentiable function , analytic function , connection (principal bundle) , variable (mathematics) , pure mathematics , several complex variables , mathematical analysis , combinatorics , geometry , holomorphic function
Interest in the study of the properties of functions defined on the set of \textit{h}-complex numbers arose again in connection with existing applications in geometry and mechanics. In this paper, we present necessary and sufficient conditions for \textit{h}-differentiability and \textit{h}-holomorphy of functions of an \textit{h}-complex variable, the theorem on finite increments is proved, sufficient conditions for \textit{h}-analyticity are found, a uniqueness theorem for \textit{h}-analytic functions is proved.