Convexity Theorem for Hyperbolic Functions in Complex Analysis
DOI:
https://doi.org/10.54097/5yfz3q63Keywords:
Hyperbolic Numbers, Convex Functions, Partial Order.Abstract
This paper studies the convexity of hyperbolic complex functions, where hyperbolic numbers are commutative rings that contain zero divisors and are composed of two real numbers. Based on the zero-divisor factorization theorem of hyperbolic numbers and other properties of functions of hyperbolic numbers, this article establishes necessary and sufficient conditions for the convexity of -differentiable functions with hyperbolic complex variables. This study, which generalizes the convexity characterization theorems from real analysis to the hyperbolic complex plane, will further establish a theoretical research foundation for the function theory of hyperbolic complex analysis and meanwhile provide impetus for the application of hyperbolic functions in physics.
Downloads
References
[1] Luna-Elizarraras M. E. Integration of Functions of a Hyperbolic Variable [J]. Complex Analysis and Operator Theory, 2022, 16 (3): 35 - 55.
[2] Abouricha A, Gourari A E, Ghanmi A. Mean Value Theorems for Bicomplex Harmonic Functions [J]. Advances in Applied Clifford Algebras, 2023, 33 (4): 41 - 56.
[3] Lino F. Resendis O, Luis M. Tovar S, Yesenia Bravo O. Conjugate complex harmonic functions [J]. Arabian Journal of Mathematics, 2023, 12 (3): 667 - 684.
[4] Matsui Y, Sato Y. Generalized self-inversive bicomplex polynomials with respect to the -conjugation [J]. Bulletin of the Korean Mathematical Society, 2021, 58 (4): 885 - 895.
[5] Lino F. Resendis O, Gamaliel Y. Tellez S, Luis M. Tovar S. Directional Derivatives and Stolz Condition for Bicomplex Holomorphic Functions [M]. Birkhauser, Cham, 2022: 201 - 207.
[6] Kuloglu, Bahar, Ozkan, Engin. Hyperbolic functions obtained from -Pell sequences [J]. Afrika matematika, 2024, 35 (1): 22 - 34.
[7] Mirosaw A, Kazimierz N. Converse Ohlin's lemma for convex and strongly convex functions [J]. Journal of Applied Analysis, 2023, 29 (1): 123 - 126.
[8] Crouzeix J. P, Hassouni A, Giannessi F, et al. A Short Note on the Twice Differentiability of the Marginal Function of a Convex Function [J]. Journal of Optimization Theory and Applications, 2023, 198 (2): 857 - 867.
[9] Ankita Chandola, Rupakshi Mishra Pandey, Kottakkaran Sooppy Nisar. On the new bic-omplex generalization of Hurwitz–Lerch zeta function with properties and applications [J]. International mathematical journal of analysis and its application, 2023, 43 (2): 71 - 88.
[10] Ortega, Yesenia Bravo, Ocampo, Lino Feliciano Resendis, Sanchez, Luis Manuel Tovar. Cousin's problems I and II: the bicomplex case [J]. Boletin de la Sociedad Matematica Mexicana, 2023, 29 (1): 99 - 116.
[11] Ghazala Akram, Maasoomah Sadaf, Saima Arshed, Muhammad Sulaiman Riaz. Exact solutions of paraxial equation via extended hyperbolic function method[J]. Optical and qua-ntum electronics, 2024, 56 (10): 1621.1 - 1621.13.
[12] Hussain Akhtar, Ibrahim Tarek F, Birkea Fathea M. Osman, Al-Sinan Bushra R. Dyna-mical behavior of analytical soliton solutions to the Kuralay equations via symbolic co-mputation [J]. Nonlinear dynamics, 2024, 112 (22): 20231 - 20254.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Highlights in Science, Engineering and Technology
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
How to Cite
