Abstract
In the paper, we have exhaustively studied the uniqueness of meromorphic function sharing two values with its \(k\)th derivative counterpart. We have obtained a series of results each of which will improve and extend a number of existing results relevant to the content of the paper. We have also pointed out some gaps in one theorem in a paper due to Chen et al. (Pure Mathematics, 8(4), 378–382 (2018) (in Chinese)) and rectifying those gaps presented the corrected form of the same in a compact manner. Thus, we have been able to streamline all the results in this particular section of literature.
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REFERENCES
B. Chen, Z. Li, and S. Li, ‘‘Uniqueness of the meromorphic function sharing two values with its derivatives,’’ Pure Math. 8 (4), 378–382 (2018). https://doi.org/10.12677/pm.2018.84051
U. Chundang and S. Tanaiadchawoot, ‘‘Meromorphic functions that share two finite values with their derivative (II),’’ Thai J. Math. 6 (1), 9–15 (2008).
G. Frank and G. Weißenborn, ‘‘Meromorphe Funktionen, die mit einer ihrer Ableitungen Werte teilen,’’ Complex Var. 7, 33–43 (1986). https://doi.org/10.1080/17476938608814184
G. G. Gundersen, ‘‘Meromorphic functions that share two finite values with their derivative,’’ Pac. J. Math. 105, 299–309 (1983). https://doi.org/10.2140/pjm.1983.105.299
W. K. Hayman, Meromorphic Functions (The Clarendon Press, Oxford, 1964).
I. Lahiri, ‘‘Value distribution of certain differential polynomials,’’ Int. J. Math. Math. Sci. 28 (2), 83–91 (2001). https://doi.org/10.1155/S0161171201011036
I. Lahiri, ‘‘Weighted value sharing and uniqueness of meromorphic functions,’’ Complex Var. 46, 241–253 (2001). https://doi.org/10.1080/17476930108815411
P. Li and C.-C. Yang, ‘‘When an entire function and its linear differential polynomial share two values,’’ Ill. J. Math. 44 (4), 349–361 (2000). https://doi.org/10.1215/ijm/1255984845
S. Li, ‘‘Meromorphic functions sharing two values IM with their derivatives,’’ Results Math. 63, 965–971 (2013). https://doi.org/10.1007/s00025-012-0246-x
E. Mues and N. Steinmetz, ‘‘Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen,’’ Manuscripta Math. 29, 195–206 (1979). https://doi.org/10.1007/BF01303627
E. Mues and N. Steinmetz, ‘‘Meromorphe Funktionen, die mit ihrer Ableitung zwei Werte teilen,’’ Results Math. 6, 48–55 (1983). https://doi.org/10.1007/BF03323323
M. Ozawa, ‘‘Unicity theorems for entire functions’’ J. Anal. Math. 30, 411–420 (1976). https://doi.org/10.1007/BF02786728
L. A. Rubel and C.-C. Yang, ‘‘Values shared by an entire function and its derivative,’’ in Complex Analysis, Ed. by J. D. Buckholtz and T. J. Suffridge (Springer, Berlin, 1977), pp. 101–103.
S. Tanaiadchawoot, ‘‘Functions that share two finite values with their derivatives,’’ Thai J. Math. 4 (2), 383–388 (2006).
Q. C. Zhang, ‘‘Uniqueness of meromorphic functions with their derivatives,’’ Acta Math. Sci. 45 (5), 871–876 (2002).
ACKNOWLEDGMENTS
The authors wish to thank the referee for his/her valuable suggestions towards the improvement of this paper.
Funding
S. Maity is supported by the Council of Scientific and Industrial Research (India), File no. 09/106(0191) /2019-EMR-I.
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Banerjee, A., Maity, S. On Two Shared Values Problem Related to Uniqueness of Meromorphic Function and Its kth Derivative. J. Contemp. Mathemat. Anal. 56, 68–79 (2021). https://doi.org/10.3103/S1068362321020035
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DOI: https://doi.org/10.3103/S1068362321020035