Transcendental entire functions of finite order sharing two sets of small functions with their shift differential operators
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.
Anahtar Kelimeler
Entire functions small function uniqueness reduced linear c-shift operator finite order
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.
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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 14 Aralık 2021 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 50 Sayı: 6 |