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Keywords:
meromorphic function; derivative; small function; weighted sharing
Summary:
In the paper we discuss the uniqueness of the $n$-th power of a meromorphic function sharing a small function with the power of its $k$-th derivative and improve and supplement a result of Zhang-Lü [Complex Var. Elliptic Equ. {53} (2008), no. 9, 857--867]. We also rectify one recent result obtained by Chen and Zhang in [Kyungpook Math. J. {50} (2010), no. 1, 71--80] dealing with a question posed by T.D. Zhang and W.R. Lü in [Complex Var. Elliptic Equ. {53} (2008), no. 9, 857--867].
References:
[1] Alzahary T.C., Yi H.X.: Weighted value sharing and a question of I. Lahiri. Complex Var. Theory Appl. 49 (2004), no. 15, 1063–1078. DOI 10.1080/02781070410001701074 | MR 2111304
[2] Banerjee A.: Meromorphic functions sharing one value. Int. J. Math. Math. Sci. 22 (2005), 3587–3598. DOI 10.1155/IJMMS.2005.3587 | MR 2205158 | Zbl 1159.30324
[3] Brück R.: On entire functions which share one value CM with their first derivative. Results Math. 30 (1996), 21–24. DOI 10.1007/BF03322176 | MR 1402421
[4] Chen A., Zhang G.: Unicity of meromorphic function and its derivative. Kyungpook Math. J. 50 (2010), no. 1, 71–80. DOI 10.5666/KMJ.2010.50.1.071 | MR 2609083
[5] Hayman W.K.: Meromorphic Functions. Clarendon Press, Oxford, 1964. MR 0164038 | Zbl 0667.30029
[6] Lahiri I.: Weighted sharing and uniqueness of meromorphic functions. Nagoya Math. J. 161 (2001), 193–206. MR 1820218 | Zbl 0981.30023
[7] Lahiri I.: Weighted value sharing and uniqueness of meromorphic functions. Complex Var. Theory Appl. 46 (2001), 241–253. DOI 10.1080/17476930108815411 | MR 1869738 | Zbl 1025.30027
[8] Lahiri I., Banerjee A.: Weighted sharing of two sets. Kyungpook Math. J. 46 (2006), no. 1, 79–87. MR 2214802 | Zbl 1103.30017
[9] Lahiri I., Sarkar A.: Uniqueness of meromorphic function and its derivative. J. Inequal. Pure Appl. Math. 5 (2004), no. 1, Article 20, http://jipam.vu.edu.au/ MR 2048496
[10] Mohon'ko A.Z.: The Nevanlinna characteristics of some meromorphic functions. Theory of Functions Funct. Anal. Appl. 14 (1971), 83–87. MR 0298006
[11] Mues E., Steinmetz N.: Meromorphe Funktionen die unit ihrer Ableitung Werte teilen. Manuscripta Math. 29 (1979), 195–206. DOI 10.1007/BF01303627 | MR 0545041
[12] Yang L.Z.: Solution of a differential equation and its applications. Kodai Math. J. 22 (1999), 458–464. DOI 10.2996/kmj/1138044097 | MR 1727305 | Zbl 1004.30021
[13] Yi H.X.: On characteristic function of a meromorphic function and its derivative. Indian J. Math. 33 (1991), no. 2, 119–133. MR 1140875 | Zbl 0799.30018
[14] Yu K.W.: On entire and meromorphic functions that share small functions with their derivatives. J. Inequal. Pure Appl. Math. 4 (2003), no. 1, Article 21, http://jipam.vu.edu.au/ MR 1966001
[15] Zhang Q.C.: The uniqueness of meromorphic functions with their derivatives. Kodai Math. J. 21 (1998), 179–184. DOI 10.2996/kmj/1138043871 | MR 1645603 | Zbl 0932.30027
[16] Zhang Q.C.: Meromorphic function that shares one small function with its derivative. J. Inequal. Pure Appl. Math. 6 (2005), no. 4, Article 116, http://jipam.vu.edu.au/ MR 2178297 | Zbl 1097.30033
[17] Zhang J.L., Yang L.Z.: Some results related to a conjecture of R. Bruck. J. Inequal. Pure Appl. Math. 8 (2007), no. 1, Article 18. MR 2295712
[18] Zhang T.D., W.R. Lü W.R.: Notes on meromorphic function sharing one small function with its derivative. Complex Var. Elliptic Equ. 53 (2008), no. 9, 857–867. DOI 10.1080/17476930802166386 | MR 2441890
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