Weakly weighted-sharing and uniqueness of homogeneous differential
polynomials

D. C. Pramanik; Ja. Roy

doi:10.15330/ms.51.1.41-49

In 2006, S. Lin and W. Lin introduced the definition of weakly weighted-sharing of meromorphic functions which is between ``CM'' and ``IM''. In this paper, using the notion of weakly weighted-sharing, we study the uniqueness of nonconstant homogeneous differential polynomials $P[f]$ and $P[g]$ generated by meromorphic functions $f$ and $g$, respectively. Our results generalize the results due to S. Lin and W. Lin, and H-Y. Xu and Y. Hu.

1. S. Bhoosnurmath, S.R. Kabbur, On entire and meromorphic functions that share one small function with their differential polynomial, Hindawi Publishing Corporation, Int. J. Analysis, 2013, Article ID 926340.

2. W.K. Hayman, Meromorphic function, Clarendon Press, Oxford, 1964.

3. I. Lahiri, B. Pal, Uniqueness of meromorphic functions with their homogeneous and linear differential polynomials sharing a small function, Bull. Korean Math. Soc., 54 (2017), 825–838.

4. S. Lin, W. Lin, Uniqueness of meromorphic functions concerning weakly weighted sharing, Kodai. Math. J., 29 (2006), 269–280.

5. H.Y. Xu, Y. Hu, Uniqueness of meromorphic function and its differential polynomial concerning weakly weighted sharing, General Mathematics, 19 (2011), 101–111.

6. L. Yang, Value distributions theory, Springer-Verlag, Berlin, 1993.

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

8. H.X. Yi, C.C. Yang, Uniqueness theory of meromorphic functions, Science Press, Beijing, 1995. (in Chinese)

	Weakly weighted-sharing and uniqueness of homogeneous differential polynomials
Author	D. C. Pramanik¹, Ja. Roy² dcpramanik.nbu2012@gmail.com¹, jayantaroy983269@yahoo.com² Department of Mathematics, University of North Bengal, Raja Rammohanpur, Darjeeling-734013, West Bengal, India
Abstract	In 2006, S. Lin and W. Lin introduced the definition of weakly weighted-sharing of meromorphic functions which is between ``CM'' and ``IM''. In this paper, using the notion of weakly weighted-sharing, we study the uniqueness of nonconstant homogeneous differential polynomials $P[f]$ and $P[g]$ generated by meromorphic functions $f$ and $g$, respectively. Our results generalize the results due to S. Lin and W. Lin, and H-Y. Xu and Y. Hu.
Keywords	meromorphic function; weakly weighted share; small function; differential polynomial
DOI	doi:10.15330/ms.51.1.41-49
Reference	1. S. Bhoosnurmath, S.R. Kabbur, On entire and meromorphic functions that share one small function with their differential polynomial, Hindawi Publishing Corporation, Int. J. Analysis, 2013, Article ID 926340. 2. W.K. Hayman, Meromorphic function, Clarendon Press, Oxford, 1964. 3. I. Lahiri, B. Pal, Uniqueness of meromorphic functions with their homogeneous and linear differential polynomials sharing a small function, Bull. Korean Math. Soc., 54 (2017), 825–838. 4. S. Lin, W. Lin, Uniqueness of meromorphic functions concerning weakly weighted sharing, Kodai. Math. J., 29 (2006), 269–280. 5. H.Y. Xu, Y. Hu, Uniqueness of meromorphic function and its differential polynomial concerning weakly weighted sharing, General Mathematics, 19 (2011), 101–111. 6. L. Yang, Value distributions theory, Springer-Verlag, Berlin, 1993. 7. C.C. Yang, On deficiencies of differential polynomials II, Math. Z., 125 (1972), 107–112. 8. H.X. Yi, C.C. Yang, Uniqueness theory of meromorphic functions, Science Press, Beijing, 1995. (in Chinese)
Pages	41-49
Volume	51
Issue	1
Year	2019
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Weakly weighted-sharing and uniqueness of homogeneous differential polynomials