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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 6

Transcendental entire functions of finite order sharing two sets of small functions with their shift differential operators

Abhijit Banerjee
Arpita Roy
Pages
1636–1651
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We have exhibited several examples relevant to the content of the paper.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Dealing with a question initiated by Liu [Meromorphic functions sharing a set with applications to difference equations, J.
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Key Findings & Data:Appl., 2009], we have investigated the situation when a finite order entire function and its shift differential operator share two sets of small functions.
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Conclusion & Impact:We have exhibited several examples relevant to the content of the paper.
🔬Design:Research Article
📍Scope:2009 Verileri
⚙️Variables:Entire functions · small function · uniqueness

Abstract

Dealing with a question initiated by Liu [Meromorphic functions sharing a set with applications to difference equations, J. Math. Anal. Appl., 2009], we have investigated the situation when a finite order entire function and its shift differential operator share two sets of small functions. Our result has improved and extended the results of Chen-Chen [Entire functions sharing sets of small functions with their difference operators or shifts, Math. Slovaca, 2013] and Cui-Chen [The conjecture on unity of meromorphic functions concerning their differences, J. Difference Equ. Appl., 2016]. We have exhibited several examples relevant to the content of the paper.

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Cite This Article

Banerjee, A., Roy, A. (2022). Transcendental entire functions of finite order sharing two sets of small functions with their shift differential operators. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 6, 1636–1651. https://ajindex.com/articles/529492

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References (9)

  1. A. Banerjee and S. Bhattacharyya, Uniqueness of meromorphic functions with their reduced linear c-shift operators sharing two or more values or sets, Adv. Difference Equ. 509, 1–23, 2019
  2. B. Chen and Z.X. Chen, Entire functions sharing sets of small functions with their difference operators or shifts, Math. Slovaca, 63 (6), 1233–1246, 2013
  3. N. Cui and Z.X. Chen, The conjecture on unity of meromorphic functions concerning their differences, J. Difference Equ. Appl. 22 (10),1452–1471, 2016
  4. R.G. Halburd and R.J. Korhonen, Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl. 314, 477– 487, 2006
  5. W.K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford 1964
  6. I. Laine and C.C. Yang, Clunie theorems for difference and q-difference polynomials, J. London Math. Soc. 76 (3), 556–566, 2007
  7. K. Liu, Meromorphic functions sharing a set with applications to difference equations, J. Math. Anal. Appl. 359, 384–393, 2009
  8. L. Yang, Value distribution theory, Springer, New York, 1993
  9. C.C. Yang and H.X. Yi, Uniqueness theory of meromorphic functions, Kluwer Aca- demic Publishers, Dordrecht, 2003.