Abstract
In this paper we prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share three sets. The obtained results improve some recent existing results.
Similar content being viewed by others
References
A. Banerjee, “On a question of Gross”, J. Math. Anal. Appl., 327 (2), 1273–1283, 2007.
A. Banerjee, “Some uniqueness results on meromorphic functions sharing three sets”, Ann. Polon. Math., 92 (3), 261–274, 2007.
A. Banerjee and P. Bhattacharjee, “Uniqueness of derivatives of meromorphic functions sharing two or three sets”, Turk. J. Math., 33, 1–14, 2009.
A. Banerjee and P. Bhattacharjee, “Uniqueness and set sharing of derivatives of meromorphic functions”, Math. Slovaca., 61 (2), 197–214, 2011.
A. Banerjee and P. Bhattacharjee, “Uniqueness of meromorphic functions that share three sets”, Kyungpook Math. J., 49, 15–19, 2009.
A. Banerjee and S. Mukherjee, “Uniqueness of meromorphic functions sharing two or three sets”, Hokkaido Math. J., 37 (3), 507–530, 2008.
M. L. Fang and W. Xu, “A note on a problem of Gross”, Chinese J. Contemporary Math., 18 (4), 395–402, 1997.
F. Gross, “Factorization of meromorphic functions and some open problems”, Proc. Conf. Univ. Kentucky, (Leixngton, Ky, 1976); Lecture Notes in Math., 599, 51–69, 1977.
F. Gross and C. C. Yang, “On preimage and range sets of meromorphic functions”, Proc. Japan Acad., 58, 17–20, 1982.
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.
I. Lahiri, “Weighted sharing and uniqueness of meromorphic functions”, Nagoya Math. J., 161, 193–206, 2001.
I. Lahiri, “Weighted value sharing and uniqueness of meromorphic functions”, Complex Var. Theory Appl., 46, 241–253, 2001.
I. Lahiri and A. Banerjee, “Uniqueness of meromorphic functions with deficient poles”, Kyungpook Math. J., 44, 575–584, 2004.
I. Lahiri and A. Banerjee, “Weighted sharing of two sets”, Kyungpook Math. J., 46, 79–87, 2006.
W. C. Lin and H. X. Yi, “Uniqueness theorems for meromorphic functions that share three sets”, Complex Var. Theory Appl., 48 (4), 315–327, 2003.
A. Z. Mokhon’ko, “On the Nevanlinna characteristics of some meromorphic functions”, Theo. Funct. Funct. Anal. Appl., Izd-vo Khar’kovsk. Un-ta, 14, 83–87, 1971.
H. Qiu and M. Fang, “A unicity theorem for meromorphic functions”, Bull. Malaysian Math. Sci. Soc., 25, 31–38, 2002.
H. X. Yi, “Uniqueness of meromorphic functions and a question of Gross”, J. Science in China (Ser A), 37 (7), 802–813, 1994.
H. X. Yi, “Meromorphic functions with weighted sharing of three values”, Complex Var., 50 (2), 923–934, 2005.
H. X. Yi, “Unicity theorems for meromorphic or entire functions”, Bull. Austral. Math. Soc., 49 (2), 257–265, 1994.
H. X. Yi and W. C. Lin, “Uniqueness theorems concerning a question ofGross”, Proc. Japan Acad., 80, Ser. A, 136–140, 2004.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A. Banerjee, S. Majumder, B. Chakraborty, 2017, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2017, No. 2, pp. 3-19.
The research is supported by the Council Of Scientific and Industrial Research, Extramural Research Division, CSIR Complex, Pusa, New Delhi-110012, India, under the sanction project no. 25(0229)/14/EMR-II.
About this article
Cite this article
Banerjee, A., Majumder, S. & Chakraborty, B. Further results on uniqueness of derivatives of meromorphic functions sharing three sets. J. Contemp. Mathemat. Anal. 52, 81–91 (2017). https://doi.org/10.3103/S1068362317020042
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1068362317020042