Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

UNIQUENESS OF q-SHIFT DIFFERENCE-DIFFERENTIAL POLYNOMIAL OF MEROMORPHIC AND ENTIRE FUNCTION WITH ZERO-ORDER

  • V. NAGARJUN (Department of Mathematics, School of Engineering, Presidency University) ;
  • V. HUSNA (Department of Mathematics, School of Engineering, Presidency University) ;
  • VEENA (Department of Mathematics,School of Engineering, Presidency University)
  • Received : 2021.12.18
  • Accepted : 2023.02.07
  • Published : 2023.03.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this article, we investigate the uniqueness problem of q-shift difference polynomial of meromorphic (entire) function with zero-order. Consequently, we prove three results with significantly generalize the results of Goutam Haldar.

Keywords

Acknowledgement

The authors wish to thank the reviewers for careful reading and valuable suggestions towards the improvement of the paper.

References

  1. J. Zhang and R. Korhonen, On the Nevanlinna characteristic of f(qz) and its applications, J. Math. Anal. Appl. 369 (2010), 537-544. https://doi.org/10.1016/j.jmaa.2010.03.038
  2. K. Liu and X.G. Qi, Meromorphic solutions of q-shift difference equations, Ann. Polon. Math. 101 (2011), 215-225. https://doi.org/10.4064/ap101-3-2
  3. K. Liu, X.L. Liu and T.B. Cao, Uniqueness and zeros of q-shift difference polynomials, Proc. Indian Acad. Sci. Math. Sci. 121 (2011), 301-310. https://doi.org/10.1007/s12044-011-0038-3
  4. H.Y. Xu, K. Liu and T.B. Cao, Uniqueness and value distribution for q-shifts of meromorphic functions, Math. Commun. 20 (2015), 97-112.
  5. I. Lahiri and S. Dewan, Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J. 26 (2003), 95-100.
  6. A.Z. Mohon'ko, On the Nevanlinna characteristics of some meromorphic functions, Func. Anal. its Appl. 14 (1971), 83-87.
  7. I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Variables Theory Appl. 46 (2001), 241-253.
  8. H.X. Yi, Meromorphic functions that share one or two values. II, Kodai Math. J. 22 (1999), 264-272. https://doi.org/10.2996/kmj/1138044046
  9. I. Lahiri and A. Banerjee, Weighted sharing of two sets, Kyungpook Math. J. 46 (2006), 79-87.
  10. L. Yang, Value distribution theory, translated and revised from the 1982 Chinese original, Springer-Verlag, Berlin, 1993.
  11. Q. Zhang, Meromorphic function that shares one small function with its derivative, JIPAM. J. Inequal. Pure Appl. Math. 6 (2005), Article 116, 13 pp.
  12. T.C. Alzahary and H.X. Yi, Weighted value sharing and a question of I. Lahiri, Complex Var. Theory Appl. 49 (2004), 1063-1078.
  13. A. Banerjee, Meromorphic functions sharing one value, Int. J. Math. Math. Sci. 2005 (2005), 3587-3598. https://doi.org/10.1155/IJMMS.2005.3587
  14. I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193-206. https://doi.org/10.1017/S0027763000027215
  15. I. Lahiri and A. Sarkar, Uniqueness of a meromorphic function and its derivative, JIPAM. J. Inequal. Pure Appl. Math. 5 (2004), Article 20, 9 pp.
  16. W.K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.
  17. A. Banerjee and M.B. Ahamed, Uniqueness of a polynomial and a differential monomial sharing a small function, An. Univ. Vest Timis. Ser. Mat.-Inform. 54 (2016), 55-71.
  18. A. Banerjee and M.B. Ahamed, Results on meromorphic function sharing two sets with its linear c-difference operator, Journal of Contemporary Mathematical Analysis 55 (2020), 143-155. https://doi.org/10.3103/S1068362320030024
  19. M.B. Ahamed, An investigation on the conjecture of Chen and Yi, Results Math. 74 (2019), 28 pp.
  20. G. Haldar, Some further q-shift difference results on Hayman Conjecture, Rendiconti del circolo Mathematico di palremo series 2, 14 June 2021.
  21. V. Husna, Results on difference polynomials of an entire function and its k-th derivative shares a small function, Journal of Physics: Conference Series 1597 (2020), 1-11. https://doi.org/10.1088/1742-6596/1597/1/012016
  22. V. Husna, Some results on uniqueness of meromorphic functions concerning differential polynomials, J. Anal. 29 (2021), 1191-1206. https://doi.org/10.1007/s41478-021-00305-w