호남수학학술지 (Honam Mathematical Journal)

  • 제46권2호
  • /
  • Pages.267-278
  • /
  • 2024
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

UNIQUENESS OF A MEROMORPHIC FUNCTION WITH DIFFERENCE POLYNOMIAL OF DIFFERENCE OPERATOR SHARING TWO VALUES CM

  • H. R. Jayarama (Department of Mathematics, School of Engineering, Presidency University) ;
  • H. Harish (Department of Mathematics, Sri Mahaveera First Grade College) ;
  • S. H. Naveenkumar (Department of Mathematics, School of Engineering, Presidency University) ;
  • C. N. Chaithra (Department of Mathematics, School of Engineering, Presidency University)
  • 투고 : 2023.10.07
  • 심사 : 2023.12.21
  • 발행 : 2024.06.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we investigate the uniqueness of a meromorphic function f(z) and its difference polynomial of difference operator with two sharing values counting multiplicities. Our two results improve and generalize the recent results of Barki Mahesh, Dyavanal Renukadevi S and Bhoosnurmath Subhas S [4] and for the case q ≥ 2, this allows for a highly unique generalization. To further demonstrate the validity of our main result, we provide an example.

키워드

참고문헌

  1. Molla Basir Ahamed, The class of meromorphic functions sharing values with their difference polynomials, Indian J. Pure Appl. Math. 54 (2023), no. 4, 1158-1169.
  2. A. Banerjee and G. Haldar, Sufficient conditions for periodicity of meromorphic function and its shift operator sharing one or more sets with finite weight, Novi Sad J. Math. 49 (2019), no. 1, 41-65.
  3. A. Banerjee and M. Basir Ahamed, Results on meromorphic function sharing two sets with its linear-difference operator, J. Contemp. Math. Anal. (Armenian Academy of Sciences) 55 (2020), no. 3, 143-155.
  4. Mahesh Barki, Renukadevi S Dyavanal, and Subhas S Bhoosnurmath, Uniqueness of a meromorphic function sharing two values cm with its difference operator, Indian J. Pure Appl. Math. 53 (2022), no. 4, 907-914.
  5. Baoqin Chen, Zongxuan Chen, and Sheng Li, Uniqueness of difference operators of meromorphic functions, J Inequal. Appl. 48 (2012), 1-9.
  6. Zong-Xuan Chen and Hong-Xun Yi, On sharing values of meromorphic functions and their differences, Results Math. 63 (2013), no. 1-2, 557-565.
  7. G. G. Gundersen, Meromorphic functions that share two finite values with their derivative, Pac. J. Math. 105 (1983), 299-309.
  8. 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 (2006), no. 2, 477-487.
  9. G. Haldar, Uniqueness of Meromorphic functions concerning k-th derivatives and difference operators, Palest. J. Math. 11 (2022), no. 3, 462-473.
  10. Walter Kurt Hayman, Meromorphic functions, 78, Oxford Clarendon Press, 1964.
  11. J. Heittokangas, R. Korhonen, I. Laine, and J. Rieppo, Uniqueness of meromorphic functions sharing values with their shifts, Complex Var. Elliptic Equ. 56 (2011), no. 1-4, 81-92.
  12. J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, and J. Zhang, Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity, J. Math. Anal. Appl. 355 (2009), no.1, 352-363.
  13. Yeyang Jiang and Zongxuan Chen, Meromorphic functions share two values with its difference operator, An. S,tiint,. Univ.'Al. I. Cuza'Ia,si, Mat. 63 (2013), no. 1, 169-175.
  14. Sujoy Majumder, Meromorphic Functions Sharing One Value with Their Derivatives Concerning the Difference Operator, Commun. Math. Stat. 5 (2017), 407-427.
  15. Erwin Mues and Norbert Steinmetz, Meromorphe funktionen, die mit ihrer ableitung werte teilen, Manuscripta Math. 29 (1979), 195-206.
  16. Erwin Mues and Norbert Steinmetz, Meromorphe funktionen, die mit ihrer ableitung zwei werte teilen, Results Math 6 (1983), 48-55.
  17. Rolf Nevanlinna, Einige eindeutigkeits atze in der theorie der meromorphen funktionen, Acta Math. 48 (1926), 367-391.
  18. Xiaoguang Qi and Kai Liu, Uniqueness and value distribution of differences of entire functions, J. Math. Anal. Appl. 379 (2011), no.1, 180-187.
  19. L. A. Rubel and Chung-Chun Yang, Values shared by an entire function and its derivative, In Complex analysis, Lecture Notes in Math. 599 (1977), 101-103.
  20. Pulak Sahoo and Himadri Karmakar, Uniqueness results related to certain q-shift difference polynomials, Annals of the Alexandru Ioan Cuza University-Mathematics 2 (2018).
  21. Chung-Chun Yang and Hong-Xun Yi, The uniqueness theory of meromorphic functions, Science press, Beijing, 1995.
  22. Chung-Chun Yang and Hong-Xun Yi, Uniqueness theory of meromorphic functions, Springer Science and Business Media 557, 2004.