Weighted Set Sharing and Uniqueness of Meromorphic Functions

In this paper, we study the uniqueness problem of meromorphic functions sharing a set of small functions and proved that under certain essential conditions $P[f]=tp(f)$ for some $t$ such that $t^m=1$ ($m$ is a positive number), where $P[f]$ is a differential polynomial in $f$ and $p(z)$ is a polynomial in $z$ of degree at least one such that $p(0)=0$. Our results generalizes the results due to Zhang and Lü}, Banerjee and Majumder, Bhoosnurmath and Kabur, and Charak and Lal.

Keywords:

Meromorphic function, shared set, small function differential polynomial.,

PDF

___

[1] T. C. Alzahary and H.-X. Yi, Weighted value sharing and a question of I. Lahiri, Complex Variables. Vol:49, No.15 (2004), 1063-1078.
[2] A. Banerjee and S. Majumder, Some uniqueness results related to meromorphic function that share a small function with its derivative, Math Reports. Vol:66 (2014), 95-111.
[3] S. Bhoosnurmath and S.R. Kabbur, On entire and meromorphic functions that share one small function with their differential polynomial, Hindawi Publishing Corporation. Intl J Analysis 2013, Article ID 926340.
[4] K. S. Charak and B. Lal, Uniqueness of p( f ) and P[ f ], Turk J Math. Vol:40 (2016), 569-581.
[5] A. A. Goldberg, I. V. Ostrovskii, Value Distribution of Meromorhic Functions, Translated from the 1970 Russian original by Mikhail Ostrovskii. With an appendix by Alexandre Eremenko and James K. Langley. Translations of Mathematical Monographs, 236. American Mathematical Society, Providence, RI, USA, 2008.
[6] G. G. Gundersen, Meromorphic functions that share finite values with their derivative, J. Math. Anal. Appl. Vol:75 (1980), 441-446.
[7] Hayman, W. K., Meromorphic Functions, Clarendon Press, Oxford, UK, 1964.
[8] I. Lahiri, Weighted sharing of two sets, Kyungpook Math. J. Vol:46 (2006), 79-87.
[9] E. Mues and N. Steinmetz, Meromorphe funktionen die unit ihrer ableitung werte teilen, Manuscripta Math. Vol:29 (1979), 195-206.
[10] Yang, L., Value Distribution Theory, Springer-Verlag, Berlin, 1993.
[11] Yang, C. C. and Yi, H. X., Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht, the Netherlands, 2003.
[12] H. X. Yi, Meromorphic function that share one or two value II, Kodai Math. J. Vol:22 (1999), 264-272.
[13] T. Zhang and W. L¨u, Notes on a meromorphic function sharing one small function with its derivative, Complex Variables and Elliptic Equations. Vol:53 (2008), 857-867.

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: Mehmet Zeki SARIKAYA

Arşiv