Meromorphic function that share a set of small functions with its derivative

P. Sahoo; G. Biswas

doi:10.15330/ms.46.2.130-136

In this paper, we investigate the uniqueness problem of meromorphic function that share a set of small functions with its derivative and obtain some results which improve and generalize the recent results due to S. Majumder [Arab J. Math. Sci., 22 (2016), 265–274].

1. A. Al-Khaladi, On meromorphic functions that share one value with their derivatives, Analysis, 25 (2005), 131–140.

2. A. Banerjee,Weighted sharing of a small function by a meromorphic function and its derivative, Comput. Math. Appl., 53 (2007), 1750–1761.

3. R. Bruck, On entire functions which share one value CM with their first derivative, Results Math., 30 (1996), 21–24.

4. Z.X. Chen, K.H. Shon, On conjecture of R. Bruck concerning entire function sharing one value CM with its derivative, Taiwanese J. Math., 8 (2004), 235–244.

5. G.G. Gundersen, Meromorphic functions that share finite values with their derivatives, J. Math. Anal. Appl., 75 (1980), 441–446.

6. G.G. Gundersen, L. Z. Yang, Entire functions that share one value with one or two of their derivatives, J. Math. Anal. Appl., 223 (1998), 88–95.

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

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

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

10. S. Majumder, Values shared by meromorphic functions and their derivatives, Arab J. Math. Sci., 22 (2016), 265–274.

11. E. Mues, N. Steinmetz, Meromorphe Funktionen, die mit ihrer und zweiten Ableitung einen endchen Wertteilen, Complex Var. Theory Appl., 6 (1986), 51–71.

12. L. Sheng, G. Zongsheng, Results on a question of Zhang and Yang, Acta Math. Sci., 32 (2012), 717–723.

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

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

15. L.Z. Yang, Entire functions that share finite values with their derivatives, Bull. Aust. Math. Soc., 41 (1990), 337–342.

16. L.Z. Yang, J.L. Zhang, Nonexistence of meromorphic solutions of Fermat type function equation, Aequations Math., 76 (2008), 140–150.

17. H.X. Yi, On characteristic function of a meromorphic function and its derivative, Indian J. Math., 33 (1991), 119–133.

18. H.X. Yi, C.C. Yang, Uniqueness theory of meromorphic functions, Science Press, Beijing, New York, 1995.

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

20. J.L. Zhang, L.Z. Yang, A power of a meromorphic function sharing a small function with its derivative, Ann. Acad. Sci, Fenn. Math., 34 (2009), 249–260.

21. Q.C. Zhang, Meromorphic function that shares one small function with its derivative, J. Inequal. Pure. Appl. Math., 6 (2005), Art. 116.

	Meromorphic function that share a set of small functions with its derivative
Author	P. Sahoo, G. Biswas Department of Mathematics, University of Kalyani, West Bengal, India sahoopulak1@gmail.com, gdb.math@gmail.com
Abstract	In this paper, we investigate the uniqueness problem of meromorphic function that share a set of small functions with its derivative and obtain some results which improve and generalize the recent results due to S. Majumder [Arab J. Math. Sci., 22 (2016), 265–274].
Keywords	meromorphic function; small function; set sharing; derivative
DOI	doi:10.15330/ms.46.2.130-136
Reference	1. A. Al-Khaladi, On meromorphic functions that share one value with their derivatives, Analysis, 25 (2005), 131–140. 2. A. Banerjee,Weighted sharing of a small function by a meromorphic function and its derivative, Comput. Math. Appl., 53 (2007), 1750–1761. 3. R. Bruck, On entire functions which share one value CM with their first derivative, Results Math., 30 (1996), 21–24. 4. Z.X. Chen, K.H. Shon, On conjecture of R. Bruck concerning entire function sharing one value CM with its derivative, Taiwanese J. Math., 8 (2004), 235–244. 5. G.G. Gundersen, Meromorphic functions that share finite values with their derivatives, J. Math. Anal. Appl., 75 (1980), 441–446. 6. G.G. Gundersen, L. Z. Yang, Entire functions that share one value with one or two of their derivatives, J. Math. Anal. Appl., 223 (1998), 88–95. 7. W.K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964. 8. I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161 (2001), 193–206. 9. I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46 (2001), 241–253. 10. S. Majumder, Values shared by meromorphic functions and their derivatives, Arab J. Math. Sci., 22 (2016), 265–274. 11. E. Mues, N. Steinmetz, Meromorphe Funktionen, die mit ihrer und zweiten Ableitung einen endchen Wertteilen, Complex Var. Theory Appl., 6 (1986), 51–71. 12. L. Sheng, G. Zongsheng, Results on a question of Zhang and Yang, Acta Math. Sci., 32 (2012), 717–723. 13. C.C. Yang, On deficiencies of differential polynomials II, Math. Z., 125 (1972), 107–112. 14. L. Yang, Value distribution theory, Springer-Verlag Berlin, 1993. 15. L.Z. Yang, Entire functions that share finite values with their derivatives, Bull. Aust. Math. Soc., 41 (1990), 337–342. 16. L.Z. Yang, J.L. Zhang, Nonexistence of meromorphic solutions of Fermat type function equation, Aequations Math., 76 (2008), 140–150. 17. H.X. Yi, On characteristic function of a meromorphic function and its derivative, Indian J. Math., 33 (1991), 119–133. 18. H.X. Yi, C.C. Yang, Uniqueness theory of meromorphic functions, Science Press, Beijing, New York, 1995. 19. J.L. Zhang, L.Z. Yang, Some results related to a conjecture of R. Bruck, J. Inequal. Pure Appl. Math., 8 (2007), Art. 18. 20. J.L. Zhang, L.Z. Yang, A power of a meromorphic function sharing a small function with its derivative, Ann. Acad. Sci, Fenn. Math., 34 (2009), 249–260. 21. Q.C. Zhang, Meromorphic function that shares one small function with its derivative, J. Inequal. Pure. Appl. Math., 6 (2005), Art. 116.
Pages	130-136
Volume	46
Issue	2
Year	2016
Journal	Matematychni Studii
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Table of content of issue	html