Schwarz's lemma on the perplex plane
DOI:
https://doi.org/10.54097/9dr4k585Keywords:
Schwarz lemma, Perplex number, Differentiable functions in perplex planeAbstract
Perplex number is an extension of complex numbers, constituting a commutative ring with zero divisors. In this paper, we primarily investigate the Schwarz lemma on the perplex plane and successfully obtain an estimation of the modulus of differentiable functions in perplex plane. Furthermore, we discuss its potential applications in complex analysis and geometric function theory. This conclusion not only offers a fresh perspective for mathematical research but also holds significant reference value for advancing studies in physics, providing valuable theoretical support for subsequent scientific investigations.
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Jerry L.R. Chandler, An introduction to the perplex number system [J]. Discrete Applied Mathematics, 2009, 157(10): 2296-2309. ISSN: 0166-218X.
Jitman, Somphong and Sangwisut, Ekkasit. The Group of Primitive Pythagorean Triples and Perplex Numbers [J]. Mathematics Magazine, 2022, 95(4):285-293.
Anwane, S. W. Special Relativity using Perplex Numbers [J]. Advances in Applied Science Research, 2021, 12(4): 16.
Liu, Bingyuan, Two applications of the Schwarz lemma [J]. arXiv: Complex Variables, 2014: n. pag.
Ni, Lei. General Schwarz Lemmata and their applications [J]. International Journal of Mathematics, 2019: n. pag..
Broder, Kyle. The Schwarz lemma in Kähler and non-Kähler geometry [J]. Asian Journal of Mathematics, 2021.
Emanuello, J. A., & Nolder, C. A. Projective Compactification of and Its Möbius Geometry [J]. *Complex Analysis and Operator Theory*, 2015, 9: 329–354.
Poodiack, R. D., & LeClair, K. J. Fundamental theorems of algebra for the perplexes [J]. *The College Mathematics Journal*, 2009, 40(5): 322–336.
Sporn, H. Pythagorean triples, complex numbers, and perplex numbers [J]. *The College Mathematics Journal*, 2017, 48(2): 115–122.
Luna-Elizarrarás, M. E., Shapiro, M., Struppa, D. C., & Vajiac, A. Bicomplex holomorphic functions: The algebra, geometry and analysis of bicomplex numbers [M]. Birkhäuser, 2015.
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