대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제59권5호
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  • Pages.1247-1253
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  • 2022
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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UNIQUE RANGE SETS WITHOUT FUJIMOTO'S HYPOTHESIS

  • Chakraborty, Bikash (Department of Mathematics Ramakrishna Mission Vivekananda Centenary College)
  • 투고 : 2021.09.22
  • 심사 : 2022.01.24
  • 발행 : 2022.09.30
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초록

This paper studies the uniqueness of two non-constant meromorphic functions when they share a finite set. Moreover, we will give an existence of unique range sets for meromorphic functions that are the zero sets of some polynomials that do not necessarily satisfy the Fujimoto's hypothesis ([6]).

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과제정보

The research work is supported by the Department of Higher Education, Science and Technology & Biotechnology, Govt. of West Bengal under the sanction order no. 1303 (sanc.)/STBT-11012(26)/17/2021-ST SEC dated 14/03/2022.

참고문헌

  1. T. T. H. An, Unique range sets for meromorphic functions constructed without an injectivity hypothesis, Taiwanese J. Math. 15 (2011), no. 2, 697-709. https://doi.org/10.11650/twjm/1500406229
  2. A. Banerjee and I. Lahiri, A uniqueness polynomial generating a unique range set and vice versa, Comput. Methods Funct. Theory 12 (2012), no. 2, 527-539. https://doi.org/10.1007/BF03321842
  3. B. Chakraborty, J. Kamila, A. K. Pal, and S. Saha, Some results on the unique range sets, J. Korean Math. Soc. 58 (2021), no. 3, 741-760. https://doi.org/10.4134/JKMS.j200235
  4. B. Chakraborty, A. K. Pal, S. Saha, and J. Kamila, Unique range sets of meromorphic functions of non-integer finite order, Asian-Eur. J. Math. https://doi.org/10.1142/S1793557122500760
  5. G. Frank and M. Reinders, A unique range set for meromorphic functions with 11 elements, Complex Variables Theory Appl. 37 (1998), no. 1-4, 185-193. https://doi.org/10.1080/17476939808815132
  6. H. Fujimoto, On uniqueness of meromorphic functions sharing finite sets, Amer. J. Math. 122 (2000), no. 6, 1175-1203. https://doi.org/10.1353/ajm.2000.0045
  7. F. Gross and C.-C. Yang, On preimage and range sets of meromorphic functions, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), no. 1, 17-20. http://projecteuclid.org/euclid.pja/1195516180 https://doi.org/10.3792/pjaa.58.17
  8. I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193-206. https://doi.org/10.1017/S0027763000027215
  9. C.-C. Yang and H.-X. Yi, Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557, Kluwer Academic Publishers Group, Dordrecht, 2003.