# On the uniqueness of a power of a meromorphic function sharing a small function with the power of its derivative

Abhijit Banerjee; Sujoy Majumder

Commentationes Mathematicae Universitatis Carolinae (2010)

- Volume: 51, Issue: 4, page 565-576
- ISSN: 0010-2628

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topBanerjee, Abhijit, and Majumder, Sujoy. "On the uniqueness of a power of a meromorphic function sharing a small function with the power of its derivative." Commentationes Mathematicae Universitatis Carolinae 51.4 (2010): 565-576. <http://eudml.org/doc/247027>.

@article{Banerjee2010,

abstract = {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].},

author = {Banerjee, Abhijit, Majumder, Sujoy},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {meromorphic function; derivative; small function; weighted sharing; meromorphic function; small function; weighted sharing},

language = {eng},

number = {4},

pages = {565-576},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {On the uniqueness of a power of a meromorphic function sharing a small function with the power of its derivative},

url = {http://eudml.org/doc/247027},

volume = {51},

year = {2010},

}

TY - JOUR

AU - Banerjee, Abhijit

AU - Majumder, Sujoy

TI - On the uniqueness of a power of a meromorphic function sharing a small function with the power of its derivative

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2010

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 51

IS - 4

SP - 565

EP - 576

AB - 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].

LA - eng

KW - meromorphic function; derivative; small function; weighted sharing; meromorphic function; small function; weighted sharing

UR - http://eudml.org/doc/247027

ER -

## References

top- Alzahary T.C., Yi H.X., 10.1080/02781070410001701074, Complex Var. Theory Appl. 49 (2004), no. 15, 1063–1078. MR2111304DOI10.1080/02781070410001701074
- Banerjee A., 10.1155/IJMMS.2005.3587, Int. J. Math. Math. Sci. 22 (2005), 3587–3598. Zbl1159.30324MR2205158DOI10.1155/IJMMS.2005.3587
- Brück R., 10.1007/BF03322176, Results Math. 30 (1996), 21–24. MR1402421DOI10.1007/BF03322176
- Chen A., Zhang G., 10.5666/KMJ.2010.50.1.071, Kyungpook Math. J. 50 (2010), no. 1, 71–80. MR2609083DOI10.5666/KMJ.2010.50.1.071
- Hayman W.K., Meromorphic Functions, Clarendon Press, Oxford, 1964. Zbl0667.30029MR0164038
- Lahiri I., Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193–206. Zbl0981.30023MR1820218
- Lahiri I., 10.1080/17476930108815411, Complex Var. Theory Appl. 46 (2001), 241–253. Zbl1025.30027MR1869738DOI10.1080/17476930108815411
- Lahiri I., Banerjee A., Weighted sharing of two sets, Kyungpook Math. J. 46 (2006), no. 1, 79–87. Zbl1103.30017MR2214802
- 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/. MR2048496
- Mohon'ko A.Z., The Nevanlinna characteristics of some meromorphic functions, Theory of Functions Funct. Anal. Appl. 14 (1971), 83–87. MR0298006
- Mues E., Steinmetz N., 10.1007/BF01303627, Manuscripta Math. 29 (1979), 195–206. MR0545041DOI10.1007/BF01303627
- Yang L.Z., 10.2996/kmj/1138044097, Kodai Math. J. 22 (1999), 458–464. Zbl1004.30021MR1727305DOI10.2996/kmj/1138044097
- Yi H.X., On characteristic function of a meromorphic function and its derivative, Indian J. Math. 33 (1991), no. 2, 119–133. Zbl0799.30018MR1140875
- 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/. MR1966001
- Zhang Q.C., 10.2996/kmj/1138043871, Kodai Math. J. 21 (1998), 179–184. Zbl0932.30027MR1645603DOI10.2996/kmj/1138043871
- 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/. Zbl1097.30033MR2178297
- 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. MR2295712
- Zhang T.D., W.R. Lü W.R., 10.1080/17476930802166386, Complex Var. Elliptic Equ. 53 (2008), no. 9, 857–867. MR2441890DOI10.1080/17476930802166386

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