Cross-sharing problems of differential polynomials of meromorphic functions
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Abstract
This paper deals with the determination of meromorphic functions for which the differential polynomials or difference-differential polynomials generated by meromorphic functions f and g share a small function with weighted sharing. The results extend and generalize those obtained by Guo and Liu [7]
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References
[1] A. Bibi, X. M. Li, and H. X. Yi, On the solutions of the differential functional equation (fn)(k)(gn)(k) = 1 and its applications, Ann. Polon. Math. 131 (2) (2023), 235–262. Google Scholar
[2] J. F. Chen, X. Y. Zhang, W. C. Lin, and S. J. Chen, Uniqueness of entire functions that share one value, Comput. Math. Appl. 56 (11) (2008), 3000–3014. Google Scholar
[3] J. Dou, X. G. Qi, and L. Z. Yang, Entire functions that share fixed points, Bull. Malays. Math. Sci. Soc. 34 (2) (2011), 355–367. Google Scholar
[4] M. L. Fang and H. Qiu, Meromorphic functions that share fixed-points, J. Math. Anal. Appl. 268 (2) (2002), 426–439. Google Scholar
[5] M. L. Fang, Uniqueness and value-sharing of entire functions, Comput. Math. Appl. 44 (5-6) (2002), 823–831. https://doi.org/10.1016/S0898-1221(02)00194-3 Google Scholar
[6] Y. C. Gao and K. Liu, Paired Hayman conjecture and uniqueness of complex delay-differential polynomials, Bull. Korean Math. Soc. 59 (1) (2022), 155–166. https://doi.org/10.4134/BKMS.b210170 Google Scholar
[7] Y. Guo and K. Liu, Zeros and uniqueness problems related to F(k) −α(z), Indian J. Pure Appl. Math. 55 (2024). https://doi.org/10.1007/s13226-024-00681-6 Google Scholar
[8] R. G. Halburd, R. J. Korhonen, and K. Tohge, Holomorphic curves with shift-invariant hyperplane preimages, Trans. Amer. Math. Soc. 366 (8) (2014), 4267–4298. Google Scholar
[9] W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford (1964). Google Scholar
[10] W. K. Hayman, Picard’s values of meromorphic functions and their derivatives, Ann. of Math. 70 (1) (1959), 9–42. https://doi.org/10.2307/1969890 Google Scholar
[11] I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl. 46 (3) (2001), 241–253. https://doi.org/10.1080/17476930108815411 Google Scholar
[12] I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193–206. https://doi.org/10.1017/S0027763000027215 Google Scholar
[13] I. Laine and C. C. Yang, Value distribution of difference polynomials, Proc. Japan Acad. Ser. A Math. Sci. 83 (5) (2007), 148–151. https://doi.org/10.3792/pjaa.83.148 Google Scholar
[14] W. C. Lin and H. X. Yi, Uniqueness theorems for meromorphic functions, Indian J. Pure Appl. Math. 35 (1) (2004), 121–132. Google Scholar
[15] K. Liu, I. Laine, and L. Z. Yang, Complex Delay-Differential Equations, De Gruyter, Berlin Boston (2021). Google Scholar
[16] D. C. Pramanik and J. Roy, Results on uniqueness of meromorphic functions weighted-sharing a set of roots of unity, J. Interdiscip. Math. 25 (1) (2022), 45–62. https://doi.org/10.1080/09720502.2021.2010766 Google Scholar
[17] F. N. Wang and K. Liu, Value cross-sharing of meromorphic functions, Comput. Methods Funct. Theory 23 (4) (2023), 807–828. https://doi.org/10.1007/s40315-023-00481-9 Google Scholar
[18] C. C. Yang, On deficiencies of differential polynomials II, Math. Z. 125 (2) (1972), 107–112. Google Scholar
[19] H. X. Yi and C. C. Yang, Uniqueness theory of meromorphic functions (in Chinese), Science Press, Beijing (1995). Google Scholar