Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

UNIQUENESS OF MEROMORPHIC FUNCTION WITH ITS k-TH DERIVATIVE SHARING TWO SMALL FUNCTIONS UNDER DIFFERENT WEIGHTS

  • Received : 2022.06.07
  • Accepted : 2022.12.22
  • Published : 2023.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

In the paper, we have exhaustively studied about the uniqueness of meromorphic function sharing two small functions with its k-th derivative as these types of results have never been studied earlier. We have obtained a series of results which will improve and extend some recent results of Banerjee-Maity [1].

Keywords

Acknowledgement

The authors wish to thank the referee for his/her valuable suggestions towards the improvement of this paper. The second author is thankful to Council of Scientific and Industrial Research (India) for their financial support under File No: 09/106(0200)/2019-EMR-I.

References

  1. A. Banerjee and S. Maity, On two shared values problem related to iniqueness of meromorphic function and its kth derivative, J. Contemp. Math. Anal. 56 (2021), no. 2, 68-79.  https://doi.org/10.3103/S1068362321020035
  2. B. Chen, Z. Li, and S. Li, Uniqueness of the meromorphic function sharing two values with its derivatives, Pure Math. 8 (2018), no. 4, 378-382.  https://doi.org/10.12677/PM.2018.84051
  3. U. Chundang and S. Tanaiadchawoot, Meromorphic functions that share two finite values with their derivative. II, Thai J. Math. 6 (2008), no. 1, 9-15. 
  4. G. Frank and G. Weissenborn, Meromorphe Funktionen, die mit einer ihrer Ableitungen Werte teilen, Complex Variables Theory Appl. 7 (1986), no. 1-3, 33-43. https://doi.org/10.1080/17476938608814184 
  5. I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193-206. https://doi.org/10.1017/S0027763000027215 
  6. I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Variables Theory Appl. 46 (2001), no. 3, 241-253. https://doi.org/10.1080/17476930108815411 
  7. P. Li and C.-C. Yang, When an entire function and its linear differential polynomial share two values, Illinois J. Math. 44 (2000), no. 2, 349-362. http://projecteuclid.org/euclid.ijm/1255984845  https://doi.org/10.1215/ijm/1255984845
  8. G. Qiu, Uniqueness of entire functions that share some small functions, Kodai Math. J. 23 (2000), no. 1, 1-11. https://doi.org/10.2996/kmj/1138044152 
  9. L. A. Rubel and C. C. Yang, Values shared by an entire function and its derivative, in Complex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976), 101-103, Lecture Notes in Math., Vol. 599, Springer, Berlin, 1977. 
  10. S. Tanaiadchawoot, Functions that share two finite values with their derivative, Thai J. Math. 4 (2006), no. 2, 383-388. 
  11. Q. C. Zhang, The uniqueness of meromorphic functions with their derivatives, Kodai Math. J. 21 (1998), no. 2, 179-184. https://doi.org/10.2996/kmj/1138043871 
  12. Q. C. Zhang, Uniqueness of meromorphic functions with their derivatives, Acta Math. Sinica (Chinese Ser.) 45 (2002), no. 5, 871-876.