Research Article
BibTex RIS Cite

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

Year 2021, Volume: 50 Issue: 6, 1636 - 1651, 14.12.2021
https://doi.org/10.15672/hujms.785797

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.

References

  • [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.
Year 2021, Volume: 50 Issue: 6, 1636 - 1651, 14.12.2021
https://doi.org/10.15672/hujms.785797

Abstract

References

  • [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.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Abhijit Banerjee 0000-0002-6160-7506

Arpıta Roy 0000-0002-4805-031X

Publication Date December 14, 2021
Published in Issue Year 2021 Volume: 50 Issue: 6

Cite

APA Banerjee, A., & Roy, A. (2021). Transcendental entire functions of finite order sharing two sets of small functions with their shift differential operators. Hacettepe Journal of Mathematics and Statistics, 50(6), 1636-1651. https://doi.org/10.15672/hujms.785797
AMA Banerjee A, Roy A. Transcendental entire functions of finite order sharing two sets of small functions with their shift differential operators. Hacettepe Journal of Mathematics and Statistics. December 2021;50(6):1636-1651. doi:10.15672/hujms.785797
Chicago Banerjee, Abhijit, and Arpıta Roy. “Transcendental Entire Functions of Finite Order Sharing Two Sets of Small Functions With Their Shift Differential Operators”. Hacettepe Journal of Mathematics and Statistics 50, no. 6 (December 2021): 1636-51. https://doi.org/10.15672/hujms.785797.
EndNote Banerjee A, Roy A (December 1, 2021) Transcendental entire functions of finite order sharing two sets of small functions with their shift differential operators. Hacettepe Journal of Mathematics and Statistics 50 6 1636–1651.
IEEE A. Banerjee and A. Roy, “Transcendental entire functions of finite order sharing two sets of small functions with their shift differential operators”, Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 6, pp. 1636–1651, 2021, doi: 10.15672/hujms.785797.
ISNAD Banerjee, Abhijit - Roy, Arpıta. “Transcendental Entire Functions of Finite Order Sharing Two Sets of Small Functions With Their Shift Differential Operators”. Hacettepe Journal of Mathematics and Statistics 50/6 (December 2021), 1636-1651. https://doi.org/10.15672/hujms.785797.
JAMA Banerjee A, Roy A. Transcendental entire functions of finite order sharing two sets of small functions with their shift differential operators. Hacettepe Journal of Mathematics and Statistics. 2021;50:1636–1651.
MLA Banerjee, Abhijit and Arpıta Roy. “Transcendental Entire Functions of Finite Order Sharing Two Sets of Small Functions With Their Shift Differential Operators”. Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 6, 2021, pp. 1636-51, doi:10.15672/hujms.785797.
Vancouver Banerjee A, Roy A. Transcendental entire functions of finite order sharing two sets of small functions with their shift differential operators. Hacettepe Journal of Mathematics and Statistics. 2021;50(6):1636-51.