Integral theorems for the quaternionic G-monogenic mappings

V. S. Shpakivskyi; T. S. Kuzmenko

doi:10.1515/auom-2016-0042

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Integral theorems for the quaternionic G-monogenic mappings

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 24 (2016): Issue 2 (June 2016)

By: V. S. Shpakivskyi and T. S. Kuzmenko

Open Access

|Sep 2017

Abstract

In the paper [1] considered a new class of quaternionic mappings, so- called G-monogenic mappings. In this paper we prove analogues of classical integral theorems of the holomorphic function theory: the Cauchy integral theorems for surface and curvilinear integrals, and the Cauchy integral formula for G-monogenic mappings.

References

[1] V. S. Shpakivskyi and T. S. Kuzmenko, On one class of quaternionic map- pings, Ukr. Math. J. 68 (1) (2016) 117-130. 10.1007/s11253-016-1213-6
Search in Google Scholar Back to article
[2] G. C. Moisil and N. Theodoresco, Functions holomorphes dans l'espace, Mathematica (Cluj), 5 (1931), 142 - 159.
Search in Google Scholar Back to article
[3] R. Fueter, Die Funktionentheorie der Di_erentialgleichungen _u = 0 und __u = 0 mit vier reellen Variablen, Comment. math. helv. 7 (1935), 307 - 330.10.1007/BF01292723
Search in Google Scholar Back to article
[4] B. Schuler, Zur Theorie der regulüaren Funktionen einer Quaternionen- Variablen, Comment. math. Helv. 10 (1937), 327 - 342.10.1007/BF01214301
Search in Google Scholar Back to article
[5] A. Sudbery, Quaternionic analysis, Math. Proc. Camb. Phil. Soc., 85 (1979), 199 - 225.10.1017/S0305004100055638
Search in Google Scholar Back to article
[6] O. F. Herus, On hyperholomorphic functions of the space variable, Ukr. Math. J. 63 (4) (2011), 530 - 537.10.1007/s11253-011-0521-0
Search in Google Scholar Back to article
[7] G. Gentili, C. Stoppato and D. Struppa, Regular Functions of a Quater- nionic Variable, Springer Monographs in Mathematics, 2013.10.1007/978-3-642-33871-7
Search in Google Scholar Back to article
[8] S. A. Plaksa and R.P. Pukhtaevich, Constructive description of mono- genic functions in n-dimensional semi-simple algebra, An. S_t. Univ. Ovidius Constant_a, 22 (1) (2014), 221 - 235.10.2478/auom-2014-0018
Search in Google Scholar Back to article
[9] I. I. Privalov, Introduction to the Theory of Functions of a Complex Vari- able, GITTL, Moscow, 1977. [in Russian]
Search in Google Scholar Back to article
[10] E. K. Blum, A theory of analytic functions in banach algebras, Trans. Amer. Math. Soc., 78 (1955), 343 - 370.10.1090/S0002-9947-1955-0069405-2
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1515/auom-2016-0042 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 271 - 281

Submitted on: Dec 17, 2014

Accepted on: Jan 7, 2015

Published on: Sep 21, 2017

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

quaternion algebra,

G-monogenic mapping,

Cauchy integral theorem,

Cauchy integral formula

Related subjects:

Mathematics,

General mathematics

© 2017 V. S. Shpakivskyi, T. S. Kuzmenko, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 24 (2016): Issue 2 (June 2016)