Mapping using p-holomorphic functions
https://doi.org/10.29235/1561-2430-2022-58-4-351-357
Abstract
In this paper, the properties of p-holomorphic maps are considered. An analog of Rolle’s theorem and a global p-diffeomorphism theorem for p-holomorphic functions are found. A modified Carathéodoryʼs theorem (conformal mapping) for p-holomorphic mappings is obtained. We prove the theorems of the mapping of rectangular domains and the compact exhaustion of bounded domains.
About the Authors
I. L. Vassilyev
Belarusian State University
Belarus
Belarus
Igor L. Vassilyev – Ph. D. (Physics and Mathematics), Associate Professor, Associate Professor of the Department of Function Theory, Belarusian State University.
4, Nezavisimosti Ave., 220030, Minsk
V. V. Dovgodilin
Belarusian State University
Belarus
Belarus
Vladimir V. Dovgodilin – Postgraduate Student of the Department of Function Theory, Belarusian State University.
4, Nezavisimosti Ave., 220030, Minsk
References
1. Yaglom I. M. Complex Numbers in Geometry. Moscow, Editorial URSS Publ., 2004. 192 p. (in Russian).
2. Messelmi F. Analysis of Dual Functions. Annual Review of Chaos Theory, Bifurcations and Dynamical Systems, 2013, vol. 4, pp. 37–54. https://doi.org/10.13140/2.1.1006.4006
3. DenHartigh K., Flim R. Liouville theorems in the Dual and Double Planes. Rose-Hulman Undergraduate Mathematics Journal, 2011, vol. 12, no. 2, pp. 37–60.
4. Dovgodilin V. Convergense on a set of p-complex numbers and properties of p-complex power series. Vestsі BDPU. Seriya 3. Fіzіka. Matematyka. Іnfarmatyka. Bіyalogіya. Geagrafіya [BGPU Bulletin. Series 3. Physics. Mathematics. Informatics. Biology. Geography], 2020, no. 4, pp. 32–39 (in Russian).
5. Vassilyev I. L., Dovgodilin V. V. On some properties of p-holomorphic and p-analytic function. Vestsі Natsyianal’nai akademіі navuk Belarusі. Seryia fіzіka-matematychnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series, 2021, vol. 57, no. 2, pp. 176–184 (in Russian). https://doi.org/10.29235/1561-2430-2021-57-2-176-184
6. Vasilyev I., Dovgodilin V. Integrals from p-complex funtions. Vestsі BDPU. Seriya 3. Fіzіka. Matematyka. Іnfarmatyka. Bіyalogіya. Geagrafіya [BGPU Bulletin. Series 3. Physics. Mathematics. Informatics. Biology. Geography], 2021, no. 2, pp. 31–36 (in Russian).
Review
Views: 271
Email this article 