On properties of h-differentiable functions

Authors

  • Vladislav Andreevich Pavlovsky Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus https://orcid.org/0000-0002-2916-1241
  • Igor Leonidovich Vasiliev Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

Keywords:

ring of h-complex numbers, zero divisors, h-differentiability, h-holomorphy, h-analyticity, finite increments of a function, zeros of a function, Taylor series

Abstract

Research in the theory of functions of an h-complex variable is of interest in connection with existing applications in non-Euclidean geometry, theoretical mechanics, etc. This article is devoted to the study of the properties of h-differentiable functions. Criteria for h-differentiability and h-holomorphy are found, formulated and proved a theorem on finite increments for an h-holomorphic function. Sufficient conditions for h-analyticity are given, formulated and proved a uniqueness theorem for h-analytic functions.

Author Biographies

  • Vladislav Andreevich Pavlovsky, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    postgraduate student at the department of function theory, faculty of mechanics and mathematics

  • Igor Leonidovich Vasiliev, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    PhD (physics and mathematics), docent; associate professor at the department of function theory, faculty of mechanics and mathematics

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Published

2021-08-05

Issue

No. 2 (2021): Journal of the Belarusian State University. Mathematics and Informatics

Section

Real, Complex and Functional Analysis

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How to Cite

[1]
Pavlovsky, V.A. and Vasiliev, I.L. 2021. On properties of h-differentiable functions. Journal of the Belarusian State University. Mathematics and Informatics. 2 (Aug. 2021), 29–37. DOI:https://doi.org/10.33581/2520-6508-2021-2-29-37.