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Year 2019, Volume: 7 Issue: 2, 243 - 251, 15.10.2019

Abstract

References

  • [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.
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  • [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.

Weighted Set Sharing and Uniqueness of Meromorphic Functions

Year 2019, Volume: 7 Issue: 2, 243 - 251, 15.10.2019

Abstract

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.

References

  • [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.
There are 13 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Dilip Pramanik

Publication Date October 15, 2019
Submission Date December 18, 2017
Acceptance Date June 19, 2019
Published in Issue Year 2019 Volume: 7 Issue: 2

Cite

APA Pramanik, D. (2019). Weighted Set Sharing and Uniqueness of Meromorphic Functions. Konuralp Journal of Mathematics, 7(2), 243-251.
AMA Pramanik D. Weighted Set Sharing and Uniqueness of Meromorphic Functions. Konuralp J. Math. October 2019;7(2):243-251.
Chicago Pramanik, Dilip. “Weighted Set Sharing and Uniqueness of Meromorphic Functions”. Konuralp Journal of Mathematics 7, no. 2 (October 2019): 243-51.
EndNote Pramanik D (October 1, 2019) Weighted Set Sharing and Uniqueness of Meromorphic Functions. Konuralp Journal of Mathematics 7 2 243–251.
IEEE D. Pramanik, “Weighted Set Sharing and Uniqueness of Meromorphic Functions”, Konuralp J. Math., vol. 7, no. 2, pp. 243–251, 2019.
ISNAD Pramanik, Dilip. “Weighted Set Sharing and Uniqueness of Meromorphic Functions”. Konuralp Journal of Mathematics 7/2 (October 2019), 243-251.
JAMA Pramanik D. Weighted Set Sharing and Uniqueness of Meromorphic Functions. Konuralp J. Math. 2019;7:243–251.
MLA Pramanik, Dilip. “Weighted Set Sharing and Uniqueness of Meromorphic Functions”. Konuralp Journal of Mathematics, vol. 7, no. 2, 2019, pp. 243-51.
Vancouver Pramanik D. Weighted Set Sharing and Uniqueness of Meromorphic Functions. Konuralp J. Math. 2019;7(2):243-51.
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