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In this article, we study the unicity of meromorphic functions concerning small functions and derivatives-differences. The results obtained in this article extend and improve some results of Chen et al. [Uniqueness problems on difference operators of meromorphic functions] and Chen and Huang [Uniqueness of meromorphic functions concerning their derivatives and shifts with partially shared values].
Słowa kluczowe
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Czasopismo
Rocznik
Tom
Strony
art. no. 20240030
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
autor
- Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China
autor
- Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China
autor
- Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China
Bibliografia
- [1] W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
- [2] I. Laine, Nevanlinna Theory and Complex Differential Equations, De Gruyter, Berlin, 1993.
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- [4] L. Yang, Value Distribution Theory, Springer-Verlag, Berlin, 1993.
- [5] Y. H. Li and J. Y. Qiao, The uniqueness of meromorphic functions concerning small functions, Sci. China Ser. A 43 (2000), 581–590.
- [6] B. Q. Chen, Z. X. Chen, and S. Li, Uniqueness theorems on entire functions and their difference operators or shifts, Abstr. Appl. Anal. 2012 (2012), no. 1, 906893, DOI: https://doi.org/10.1155/2012/906893.
- [7] C. X. Chen and Z. X. Chen, Uniqueness of meromorphic functions and their differences, Acta Math. Sinica (Chin. Ser.) 59 (2016), 821–834.
- [8] C. X. Chen, R. R. Zhang, Z. B. Huang, and S. Land, Uniqueness problems on difference operators of meromorphic functions, Sci. Asia 46 (2020), 361–367, DOI: https://doi.org/10.2306/scienceasia1513-1874.2020.045.
- [9] W. J. Chen and Z. G. Huang, Uniqueness of meromorphic functions concerning their derivatives and shifts with partially shared values, J. Contemp. Math. Anal. 57 (2022), no. 4, 232–241, DOI: https://doi.org/10.3103/S1068362322040033.
- [10] A. E. Farissi, Z. Latreuch, and A. Asiri, On the uniqueness theory of entire functions and their difference operators, Complex Anal. Oper. Theory 10 (2016), 1317–1327, DOI: https://doi.org/10.1007/s11785-015-0514-3.
- [11] J. Heittokangas, R. Korhonen, I. Laine, and J. Rieppo, Uniqueness of meromorphic functions sharing values with their shifts, Complex Var. Elliptic Equ. 56 (2011), 81–92, DOI: https://doi.org/10.1080/17476930903394770.
- [12] X. H. Huang and D. Liu, Uniqueness of entire functions that share small function with their difference polynomials, Pure Math. 9 (2019), 362–369.
- [13] Z. Y. He, J. B. Xiao, and M. L. Fang, Unicity of meromorphic functions concerning differences and small functions, Open Math. 20 (2022), 447–459, DOI: https://doi.org/10.1515/math-2022-0033.
- [14] X. G. Qi and L. Z. Yang, Uniqueness of meromorphic functions concerning their shifts and derivatives, Comput. Methods Funct. Theory 20 (2020), 159–178, DOI: https://doi.org/10.1007/s40315-020-00304-1.
- [15] L. A. Rubel and C. C. Yang, Values shared by an entire function and its derivative, Complex Analysis, Lecture Notes in Mathematics, Springer, Berlin vol. 599, 1977, pp. 101–103.
- [16] E. Mues and N. Steinmetz, Meromorphic Funktionen, die mit ihrer Ableitung Werte teilen, Manuscripta Math. 29 (1979), 195–206.
- [17] G. G. Gundersen, Meromorphic functions that share two finite values with their derivative, Pacific J. Math. 105 (1983), 299–309.
- [18] G. Frank and G. Weißenborn, Meromorphic functions that share finite values with one of their derivatives, Complex Variables Theory Appl. 7 (1986), 33–43.
- [19] G. Frank and W. Ohlenroth, Meromorphic functions which share values with one of their derivatives, Complex Variables Theory Appl. 6 (1986), 23–37.
- [20] P. Li and C. C. Yang, When an entire function and its linear differential polynomial share two values, Illinois J. Math. 44 (2000), 349–362, DOI: https://doi.org/10.1215/ijm/1255984845.
- [21] M. L. Fang, Uniqueness of meromorphic functions connected with differential polynomials, Adv. Math. (China) 24 (1995), 244–249.
- [22] Y. M. Chiang and S. J. Feng, On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plan, Ramanujan J. 16 (2008), 105–129.
- [23] R. G. Halburd and R. J. Korhonen, Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl. 314 (2006), 477–487, DOI: https://doi.org/10.1016/j.jmaa.2005.04.010.
- [24] R. G. Halburd, R. J. Korhonen, and K. Tohge, Holomorphic curves with shift-invariant hyperplane preimages, Trans. Amer. Math. Soc. 366 (2014), 4267–4298, DOI: https://doi.org/10.1090/S0002-9947-2014-05949-7.
- [25] G. Jank, E. Mues, and L. Volkmann, Meromorphic functions which share a finite value with their first and second derivative, Complex Var. Theory Appl. 6 (1986), 51–71.
- [26] Y. M. Chiang and S. J. Feng, On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions, Trans. Amer. Math. Soc. 361 (2009), 3767–3791, DOI: https://doi.org/10.1090/S0002-9947-09-04663-7.
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Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2026).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-cc1ce4c9-f734-494d-9279-8eb2b3124bdc
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