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Some properties of bicomplex holomorphic functions | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 3، دوره 16، شماره 5، مرداد 2025، صفحه 27-33 اصل مقاله (338.85 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.33970.5071 | ||
| نویسندگان | ||
| Mahmood Bidkham* 1؛ Abdollah Mir2 | ||
| 1Department of Mathematics, Semnan University, Semnan, Iran | ||
| 2Department of Mathematics, University of Kashmir, Srinagar, 190006, India | ||
| تاریخ دریافت: 11 اسفند 1402، تاریخ پذیرش: 05 خرداد 1403 | ||
| چکیده | ||
| In this paper, we first establish the bicomplex version of Rouche's theorem. Also, a new approach is given to prove the maximum modulus principle for bicomplex holomorphic functions. Our proof is based on the direct method and extends the result proved by Luna-Elizarraras et al. Finally, we generalize the Hurwitz's theorem to bicomplex space. | ||
| کلیدواژه‌ها | ||
| Bicomplex Function؛ Rouche's Theorem؛ Maximum Modulus Principle؛ Hurwitz's theorem | ||
| مراجع | ||
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[1] D. Alpay, M.E. Luna-Elizarraras, M. Shapiro, and D.C. Struppa, Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis, Springer Briefs in Mathematics, 2014. [2] K.S. Charak and D. Rochon, On the factorization of bicomplex meromorphic functions, Trends in Mathematics, Birkhauser Verlag Basel/Switzerland, 2008, pp. 55–68. [3] K.S. Charak, D. Rochon, and N. Sharma, Normal families of bicomplex holomorphic functions, Fractals 17 (2009), no. 3. [4] M.E. Luna-Elizarraras, M. Shapiro, D.C. Struppa, and A. Vajiac, Bicomplex number and their elementary function, CUBO Math. J. 14 (2012), no. 2, 61–80. [5] M. Marden, Geometry of Polynomials, 2nd ed., Mathematical Surveys, vol. 3, Amer. Math. Soc, Providence, R.I., 1966. [6] A.A. Pogorui and R.M. Rodriguez-Dagnino, On the set of zeros of bicomplex polynomials, Complex Variab. Elliptic Equ. 51 (2006), no. 7, 725–730. [7] S. Ponnusamy and H. Silverman, Complex Variables with Applications, Springer Science & Business Media, 2007. [8] R.D. Poodiack and K.J. LeClair, Fundamental theorems of algebra for the perplexes, College Math. J. 40 (2009), no. 5, 322–335. [9] G.B. Price, An Introduction to Multicomplex Spaces and Functions, Monographs and Textbooks in Pure and Applied Mathematics, vol. 140, Marcel Dekker, Inc., New York, 1991. [10] J.D. Riley, Contributions to the theory of functions of a bicomplex variable, Tohoku Math. J. Second Ser. 2 (1953), no. 5, 132–165. [11] C. Segre, Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici (The real representation of complex elements and hyper algebraic entities), Math. Ann. 40 (1892), 413–467. | ||
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