Meromorphic functions whose certain differential polynomial share a polynomial
Main Article Content
Abstract
In this paper, we use the idea of normal family to investigate the uniqueness
problems of meromorphic functions when certain non-linear dierential polynomial sharing
a nonzero polynomial with certain degree. We obtain some results which will not only rectify
the recent results of P. Sahoo and H. Karmakar [9] but also improve and generalize some
recent results of L. Liu [7], H. Y. Xu, T. B. Cao and S. Liu [12] and P. Sahoo and H.
Karmakar [9] in a large extent.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
References
A. Banerjee and S. Majumder, Certain nonlinear differential polynomial sharing a nonzero polynomial IM,
Tsukuba J.Math., 39 (2015), 221–250.
J. M. Chang and L. Zalcman, Meromorphic functions that share a set with their derivatives, J. Math. Anal.
Appl., 338 (2008), 1191–1205.
H. H. Chen, Yoshida functions and Picad values of integral functions and their derivatives, Bull. Aust. Mat.
soc., 54 (1996), 373–381.
M. L. Fang, Uniqueness and value-sharing of entire functions, Comput.Math. Appl., 44 (2002), 823–831.
W. K. Hayman,Meromorphic Functions, The Clarendon Press, Oxford (1964).
I. Lahiri, Value distribution of certain differential polynomials, Int. J.Math.Math. Sci., 28 (2001), 83–91.
L. Liu, Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl., 56 (2008),
–3245.
S.Majumder, Uniqueness and value-sharing ofmeromorphic functions with finiteweight, Analysis, 34 (2014),81–109.
X. C. Pang, Normality conditions for differential polynomials, Kexue Tongbao, 33 (1988), 1690-1693 (in Chinese).
P. Sahoo and H. Karmakar, Uniqueness of meromorphic functions whose nonlinear differential polynomialsshare a polynomial, Boll. UnioneMat. Ital., DOI 10.1007/s40574-016-0062-4.
J. Schiff, Normal Families, Berlin, 1993.
J. F. Xu, F. Lü and H. X. Yi, Fixed points and uniqueness of meromorphic functions, Comput. Math. Appl., 59(2010), 9–17.
H. Y. Xu, T. B. Cao and S. Liu, Uniqueness results ofmeromorphic functions whose nonlinear differential poly-
nomials have one nonzero pseudo value,Mat. Vesnik., 64 (2012), 1–16.
C. C. Yang, On deficiencies of differential polynomials II,Math. Z., 125 (1972), 107–112.
C. C. Yang, H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht/Boston/London, 2003.
K. Yamanoi, The secondmain theoremfor small functions and related problems, ActaMath., 192 (2004), 225–294.
H. X. Yi, On characteristic function of a meromorphic function and its derivative, Indian J. Math., 33 (1991),
–133.
L. Zalcman, Normal families, new perspectives, Bull. Amer.Math. Soc., 35 (1998), 215–230.
L. Zalcman, A heuristic principle in complex theory, Amer.Math.Monthly, 82 (1975), 813–817.
Q. C. Zhang, Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl.
Math., 6 (2005), Art.116 [ONLINEhttp://jipam.vu.edu.au/].
X. B. Zhang and J. F. Xu, Uniqueness of meromorphic functions sharing a small function and its applications,
Comput.Math. Appl., 61 (2011), 722–730.