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UNIQUENESS OF DIFFERENCE-DIFFERENTIAL POLYNOMIALS OF ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION

Year 2017, Volume: 5 Issue: 2, 119 - 130, 15.10.2017

Abstract

In this paper, we investigate the uniqueness problem of difference-differential polynomials sharing a small function with finite weight. The results of the paper improve and generalize the recent results due to Pulak Sahoo and the present author [Applied Mathematics E-Notes 16(2016), 33-44]

References

  • [1] A. Banerjee, Meromorphic functions sharing one value, Int. J. Math. Math. Sci., Vol:22, (2005), 3587-3598.
  • [2] S.S. Bhoosnurmath and S.R. Kabbur, Value distribution and uniqueness theorems for difference of entire and meromorphic functions, Int. J. Anal. Appl., Vol:2, (2013), 124-136.
  • [3] Y.M. Chiang and S.J. Feng, On the Nevanlinna characteristic of $f(z + \eta )$ and difference equations in the complex plane, Ramanujan J., Vol:16, (2008), 105-129.
  • [4] R.G. Halburd and R.J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math., Vol:31, (2006), 463-478.
  • [5] R.G. Halburd and R.J. Korhonen, Di erence analogue of the lemma on the logarithmic derivative with application to difference equations, J. Math. Anal. Appl., Vol:314, (2006), 477-487.
  • [6] R.G. Halburd and R.J. Korhonen, Meromorphic solutions of difference equations, integrability and the discrete painleve equations, J. Phys. A. Math. Theor., Vol:40, (2007), 1-38.
  • [7] W.K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs Clarendon Press, Oxford 1964.
  • [8] L. Kai, L.Xin-ling and C.Ting-bin, Some results on zeros and uniqueness of difference differential polynomials, Appl. Math. J. Chinese Univ., Vol:27, (2012), 94-104.
  • [9] I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., Vol:46, (2001), 241-253.
  • [10] I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin/Newyork, 1993.
  • [11] I. Laine and C.C. Yang, Value distribution of difference polynomials, Proc. Japan Acad. SerA Math. Sci., Vol:83, (2007), 148-151.
  • [12] X. Luo and W.C. Lin, Value sharing results for shifts of meromorphic functions, J. Math. Anal. Appl., Vol:377, (2011), 441-449.
  • [13] X.G. Qi, L.Z. Yang and K. Liu, Uniqueness and periodicity of meromorphic functions concerning the difference operator, Comput. Math. Appl., Vol:60, (2010), 1739-1746.
  • [14] P. Sahoo and B. Saha, Value Distribution and uniqueness of certain type of difference polynomials, Applied Mathematics E-Notes, Vol:16, (2016), 33-44.
  • [15] C.C. Yang and H.X. Yi, Uniqueness Theory of Meromorphic of Functions, Science Press (Beijing/New York) and Kluwer Academic Publishers (Dordrecht/Boston/London), (2003).
  • [16] L.Yang, Value Distribution Theory, Springer- Verlag, Berlin, 1993.
  • [17] J.L. Zhang, Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl., Vol:367, (2010), 401-408.
  • [18] J.L. Zhang and L.Z. Yang, Some results related to a conjecture of R. Bruck, J. Inequal. Pure Appl. Math., Vol:8, (2007), Art. 18.
Year 2017, Volume: 5 Issue: 2, 119 - 130, 15.10.2017

Abstract

References

  • [1] A. Banerjee, Meromorphic functions sharing one value, Int. J. Math. Math. Sci., Vol:22, (2005), 3587-3598.
  • [2] S.S. Bhoosnurmath and S.R. Kabbur, Value distribution and uniqueness theorems for difference of entire and meromorphic functions, Int. J. Anal. Appl., Vol:2, (2013), 124-136.
  • [3] Y.M. Chiang and S.J. Feng, On the Nevanlinna characteristic of $f(z + \eta )$ and difference equations in the complex plane, Ramanujan J., Vol:16, (2008), 105-129.
  • [4] R.G. Halburd and R.J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math., Vol:31, (2006), 463-478.
  • [5] R.G. Halburd and R.J. Korhonen, Di erence analogue of the lemma on the logarithmic derivative with application to difference equations, J. Math. Anal. Appl., Vol:314, (2006), 477-487.
  • [6] R.G. Halburd and R.J. Korhonen, Meromorphic solutions of difference equations, integrability and the discrete painleve equations, J. Phys. A. Math. Theor., Vol:40, (2007), 1-38.
  • [7] W.K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs Clarendon Press, Oxford 1964.
  • [8] L. Kai, L.Xin-ling and C.Ting-bin, Some results on zeros and uniqueness of difference differential polynomials, Appl. Math. J. Chinese Univ., Vol:27, (2012), 94-104.
  • [9] I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., Vol:46, (2001), 241-253.
  • [10] I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin/Newyork, 1993.
  • [11] I. Laine and C.C. Yang, Value distribution of difference polynomials, Proc. Japan Acad. SerA Math. Sci., Vol:83, (2007), 148-151.
  • [12] X. Luo and W.C. Lin, Value sharing results for shifts of meromorphic functions, J. Math. Anal. Appl., Vol:377, (2011), 441-449.
  • [13] X.G. Qi, L.Z. Yang and K. Liu, Uniqueness and periodicity of meromorphic functions concerning the difference operator, Comput. Math. Appl., Vol:60, (2010), 1739-1746.
  • [14] P. Sahoo and B. Saha, Value Distribution and uniqueness of certain type of difference polynomials, Applied Mathematics E-Notes, Vol:16, (2016), 33-44.
  • [15] C.C. Yang and H.X. Yi, Uniqueness Theory of Meromorphic of Functions, Science Press (Beijing/New York) and Kluwer Academic Publishers (Dordrecht/Boston/London), (2003).
  • [16] L.Yang, Value Distribution Theory, Springer- Verlag, Berlin, 1993.
  • [17] J.L. Zhang, Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl., Vol:367, (2010), 401-408.
  • [18] J.L. Zhang and L.Z. Yang, Some results related to a conjecture of R. Bruck, J. Inequal. Pure Appl. Math., Vol:8, (2007), Art. 18.
There are 18 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

BISWAJIT Saha This is me

Publication Date October 15, 2017
Submission Date October 15, 2017
Acceptance Date May 31, 2017
Published in Issue Year 2017 Volume: 5 Issue: 2

Cite

APA Saha, B. (2017). UNIQUENESS OF DIFFERENCE-DIFFERENTIAL POLYNOMIALS OF ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION. Konuralp Journal of Mathematics, 5(2), 119-130.
AMA Saha B. UNIQUENESS OF DIFFERENCE-DIFFERENTIAL POLYNOMIALS OF ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION. Konuralp J. Math. October 2017;5(2):119-130.
Chicago Saha, BISWAJIT. “UNIQUENESS OF DIFFERENCE-DIFFERENTIAL POLYNOMIALS OF ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION”. Konuralp Journal of Mathematics 5, no. 2 (October 2017): 119-30.
EndNote Saha B (October 1, 2017) UNIQUENESS OF DIFFERENCE-DIFFERENTIAL POLYNOMIALS OF ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION. Konuralp Journal of Mathematics 5 2 119–130.
IEEE B. Saha, “UNIQUENESS OF DIFFERENCE-DIFFERENTIAL POLYNOMIALS OF ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION”, Konuralp J. Math., vol. 5, no. 2, pp. 119–130, 2017.
ISNAD Saha, BISWAJIT. “UNIQUENESS OF DIFFERENCE-DIFFERENTIAL POLYNOMIALS OF ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION”. Konuralp Journal of Mathematics 5/2 (October 2017), 119-130.
JAMA Saha B. UNIQUENESS OF DIFFERENCE-DIFFERENTIAL POLYNOMIALS OF ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION. Konuralp J. Math. 2017;5:119–130.
MLA Saha, BISWAJIT. “UNIQUENESS OF DIFFERENCE-DIFFERENTIAL POLYNOMIALS OF ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION”. Konuralp Journal of Mathematics, vol. 5, no. 2, 2017, pp. 119-30.
Vancouver Saha B. UNIQUENESS OF DIFFERENCE-DIFFERENTIAL POLYNOMIALS OF ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION. Konuralp J. Math. 2017;5(2):119-30.
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