Araştırma Makalesi
BibTex RIS Kaynak Göster

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

Yıl 2021, Cilt: 50 Sayı: 6, 1636 - 1651, 14.12.2021
https://doi.org/10.15672/hujms.785797

Öz

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.

Kaynakça

  • [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.
Yıl 2021, Cilt: 50 Sayı: 6, 1636 - 1651, 14.12.2021
https://doi.org/10.15672/hujms.785797

Öz

Kaynakça

  • [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.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Abhijit Banerjee 0000-0002-6160-7506

Arpıta Roy 0000-0002-4805-031X

Yayımlanma Tarihi 14 Aralık 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 50 Sayı: 6

Kaynak Göster

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. Aralık 2021;50(6):1636-1651. doi:10.15672/hujms.785797
Chicago Banerjee, Abhijit, ve 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, sy. 6 (Aralık 2021): 1636-51. https://doi.org/10.15672/hujms.785797.
EndNote Banerjee A, Roy A (01 Aralık 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 ve 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, c. 50, sy. 6, ss. 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 (Aralık 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 ve 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, c. 50, sy. 6, 2021, ss. 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.