Entire functions that share a polynomial with finite weight

P. Sahoo; B. Saha

doi:10.15330/ms.44.1.36-44

In this paper, with the aid of weighted sharing method we study the uniqueness problems of entire functions that share a nonconstant polynomial with weight two. The results of the paper improve and generalize some results due to [10] and [11].

1. J. Dou, X.G. Qi, L.Z. Yang, Entire functions that share fixed points, Bull. Malays. Math. Sci. Soc., 34 (2011), 355–367.

2. M.L. Fang, Uniqueness and value sharing of entire functions, Comput. Math. Appl., 44 (2002), 828–831.

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

4. M.L. Fang, H.L. Qiu, Meromorphic functions that share fixed points, J. Math. Anal. Appl., 268 (2002), 426–439.

5. W.K. Hayman, Picard values of meromorphic functions and their derivatives, Ann. of Math., 70 (1959), 9–42.

6. W.K. Hayman, Meromorphic functions. – Clarendon Press, Oxford, 1964.

7. I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161 (2001), 193–206.

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

9. W.C. Lin, H.X. Yi, Uniqueness theorems for meromorphic function concerning fixed points, Complex Var. Theory Appl., 49 (2004), 793–806.

10. X.G. Qi, L.Z. Yang, Uniqueness of entire functions and fixed points, Ann. Polon. Math., 97 (2010), 87–100.

11. P. Sahoo, Entire functions that share fixed points with finite weights, Bull. Belg. Math. Soc. Simon Stevin, 18 (2011), 883–895.

12. C.C. Yang, On deficiencies of differential polynomials II, Math. Z., 125 (1972), 107–112.

13. L. Yang, Value distribution theory. – Springer-Verlag, Berlin, 1993.

14. H.X. Yi, C.C. Yang, Uniqueness theory of meromorphic functions. – Science Press, Beijing, 1995.

15. J.L. Zhang, Uniqueness theorems for entire functions concerning fixed points, Comput. Math. Appl., 56 (2008), 3079–3087.

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

	Entire functions that share a polynomial with finite weight
Author	P. Sahoo, B. Saha sahoopulak@yahoo.com, sahoopulak1@gmail.com; sahaanjan11@gmail.com Department of Mathematics, University of Kalyani; Department of Mathematics, Ghurni High School(H.S), Krishnagar West Bengal, India
Abstract	In this paper, with the aid of weighted sharing method we study the uniqueness problems of entire functions that share a nonconstant polynomial with weight two. The results of the paper improve and generalize some results due to [10] and [11].
Keywords	uniqueness; entire function; weighted sharing
DOI	doi:10.15330/ms.44.1.36-44
Reference	1. J. Dou, X.G. Qi, L.Z. Yang, Entire functions that share fixed points, Bull. Malays. Math. Sci. Soc., 34 (2011), 355–367. 2. M.L. Fang, Uniqueness and value sharing of entire functions, Comput. Math. Appl., 44 (2002), 828–831. 3. M.L. Fang, X.H. Hua, Entire functions that share one value, J. Nanjing Univ. Math. Biquarterly, 13 (1996), 44–48. 4. M.L. Fang, H.L. Qiu, Meromorphic functions that share fixed points, J. Math. Anal. Appl., 268 (2002), 426–439. 5. W.K. Hayman, Picard values of meromorphic functions and their derivatives, Ann. of Math., 70 (1959), 9–42. 6. W.K. Hayman, Meromorphic functions. – Clarendon Press, Oxford, 1964. 7. I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161 (2001), 193–206. 8. I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46 (2001), 241–253. 9. W.C. Lin, H.X. Yi, Uniqueness theorems for meromorphic function concerning fixed points, Complex Var. Theory Appl., 49 (2004), 793–806. 10. X.G. Qi, L.Z. Yang, Uniqueness of entire functions and fixed points, Ann. Polon. Math., 97 (2010), 87–100. 11. P. Sahoo, Entire functions that share fixed points with finite weights, Bull. Belg. Math. Soc. Simon Stevin, 18 (2011), 883–895. 12. C.C. Yang, On deficiencies of differential polynomials II, Math. Z., 125 (1972), 107–112. 13. L. Yang, Value distribution theory. – Springer-Verlag, Berlin, 1993. 14. H.X. Yi, C.C. Yang, Uniqueness theory of meromorphic functions. – Science Press, Beijing, 1995. 15. J.L. Zhang, Uniqueness theorems for entire functions concerning fixed points, Comput. Math. Appl., 56 (2008), 3079–3087. 16. J.L. Zhang, L.Z. Yang, Some results related to a conjecture of R. Bruck, J. Inequal. Pure Appl. Math., 8 (2007), Art. 18.
Pages	36-44
Volume	44
Issue	1
Year	2015
Journal	Matematychni Studii
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Table of content of issue	html