Some results on uniqueness of entire functions concerning difference polynominals

Article Sidebar

PDF
Published: Jun 30, 2018
DOI: https://doi.org/10.5556/j.tkjm.49.2018.2198
Keywords:
Uniqueness entire function small function difference polynomial.

Main Article Content

Pulak Sahoo
Gurudas Biswas

Abstract

In the paper we use the notion of weakly weighted sharing and relaxed weighted sharing to investigate the uniqueness problems when two difference products of entire functions share a small function. The results of the paper improve and extend some recent results due to the present first author [Commu. Math. Stat., 3 (2015), 227-238].

Article Details

How to Cite
Sahoo, P., & Biswas, G. (2018). Some results on uniqueness of entire functions concerning difference polynominals. Tamkang Journal of Mathematics, 49(2), 85–97. https://doi.org/10.5556/j.tkjm.49.2018.2198
Issue
Vol. 49 No. 2 (2018)
Section
Papers
Author Biographies

Pulak Sahoo

Department of Mathematics, University of Kalyani

Gurudas Biswas

University Research Scholar, University of Kalyani

References

A. Banerjee and S. Mukherjee, Uniqueness of meromorphic functions concerning differential monomials sharing the same value, Bull. Math. Soc. Sci. Math. Roum. Nouv. Ser., 50 (2007), 191-206.

S.S. Bhoosnurmath and S.R. Kabbur, Value distribution and uniqueness theorems for difference of entire and meromorphic functions, Int. J. Anal. Appl., 2 (2013), 124-136.

M.R. Chen and Z.X. Chen, Properties of difference polynomials of entire functions with finite order, Chinese Annals of Mathematics, 33 (2012), 359-374.

Y.M. Chiang and S.J. Feng, On the Nevanlinna characteristic of f(z +n ) and difference equations in the complex plane, Ramanujan J., 16 (2008), 105-129.

M.L. Fang and W. Hong, A unicity theorem for entire functions concerning differential polynomials, Indian J. Pure Appl. Math., 32 (2001), 1343-1348.

M.L. Fang and X.H. Hua, Entire functions that share one value, J. Nanjing Univ. Math. Biquarterly, 13(1996), 44-48.

R.G. Halburd and R.J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math., 31 (2006), 463-478.

R.G. Halburd and R.J. Korhonen, Difference analogue of the lemma on the logarithmic derivative with application to difference equations, J. Math. Anal. Appl., 314 (2006), 477-487.

W.K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).

I. Lahiri, Value distribution of certain differential polynomials, Int. J. Math. Math. Sc., 28 (2001), 83-91.

I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46 (2001), 241-253.

I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin/Newyork, 1993.

I. Laine and C.C. Yang, Value distribution of difference polynomials, Proc. Japan Acad. SerA Math. Sci., 83 (2007), 148-151.

S.H. Lin and W.C. Lin, Uniqueness of meromorphic functions concerning weakly weighted sharing, Kodai Math. J., 29 (2006), 269-280.

W.C. Lin and H.X. Yi, Uniqueness theorems for meromorphic functions concerning fixed points, Complex Variables Theory Appl., 49 (2004), 793-806.

X.Q. Lin and W.C. Lin, Uniqueness of entire functions sharing one value, Acta Math. Sci., Ser. B. Engl.Ed. 31 (2011), 1062-1076.

K. Liu and L.Z. Yang, Value distribution of the difference operator, Arch. Math. (Basel), 92 (2009), 270-278.

C. Meng, Uniqueness of entire functions concerning difference polynomials, Math. Bohemica, 139 (2014), 89-97.

X.G. Qi, L.Z. Yang and K. Liu, Uniqueness and periodicity of meromorphic functions concerning the difference operator, Computers and Mathematics with Applications, 60 (2010), 1739-1746.

P. Sahoo, Unicity theorem for entire functions sharing one value, Filomat, 27 (2013), 797-809.

P. Sahoo, Uniqueness of entire functions related to difference polynomials, Commu. Math. Stat., 3 (2015), 227-238.

P. Sahoo and S. Seikh, Meromorphic functions whose certain differential polynomials share a small function with finite weight, Analysis (Munich), 33 (2013), 143-157.

C.C. Yang and X.H. Hua, Uniqueness and value sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math., 22 (1997), 395-406.

C.C. Yang and H.X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer, Dordrecht, 2003.

J.L. Zhang, Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl., 367 (2010), 401-408.

J.L. Zhang and L.Z. Yang, Some results related to a conjecture of R. Bruck, J. Inequal. Pure Appl. Math., 8 (2007), Art. 18.