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ABHIJIT BANERJEE AND SANJAY MALLICK

Year 2016, Volume: 65 Issue: 1, 71 - 86, 01.02.2016
https://doi.org/10.1501/Commua1_0000000745

Abstract

The purpose of the paper is to obtain some su¢ cient conditions forwhich two differential polynomials sharing a small function satisfies conclusionsof Brück [3] conjecture. The result present in the paper will unify, improve andgeneralize several existing results. We have exhibited a number of examples toshow that some conditions used in the paper are essential. In the concludingpart of the paper we propose two open problems for further investigations

References

  • T. C. Alzahary and H. X. Yi, Weighted value sharing and a question of I.Lahiri, Complex Var. Theory Appl., 49(15) (2004), 1063-1078.
  • A. Banerjee, Meromorphic functions sharing one value, Int. J. Math. Math. Sci., 22(2005), 3598.
  • R. Brück, On entire functions which share one value CM with their …rst derivative, Results Math., 30(1996), 21-24.
  • C. T. Chuang, On diğ erential polynomials, Analysis of one complex variable, (Laramie, Wyo., ), 12-32, World Sci. Publishing Singapore, (1987).
  • W. Doeringer, Exceptional values of diğ erential polynomials, Paci…c J. Math., 98(1)(1982), 62.
  • G. G. Gundersen and L. Z. Yang, Entire functions that share one value with one or two of their derivatives, J. Math. Anal. Appl., 223(1)(1998), 88-95.
  • W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, (1964).
  • I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., (2001), 193-206.
  • I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46(2001), 241-253.
  • I. Lahiri and A. Banerjee, Weighted sharing of two sets, Kyungpook Math. J., 46(1)(2006), 87.
  • I. Lahiri and S. Dewan, Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J., (2003), 95-100.
  • I. Lahiri and A. Sarkar, Uniqueness of meromorphic function and its derivative, J. Inequal. Pure Appl. Math., 5(1)(2004), Art.20 [ONLINE http://jipam.vu.edu.au/].
  • L. Liu, Uniqueness of meromorphic functions that share one small function with their deriv- atives, J.Math. Sci. : Adv. Appl., 6(2)(2010), 241-255.
  • N. Li and L. Z. Yang, Meromorphic function that shares one small function with its diğ er- ential polynomial, Kyungpook Math. J., 50(2010), 447-454.
  • A. Z. Mohon’ko, On the Nevanlinna characteristics of some meromorphic functions, Theory of Functions, Functional Analysis and Their Applications, 14(1971), 83-87.
  • E. Mues and N. Steinmetz, Meromorphe funktionen die unit ihrer ableitung werte teilen, Manuscripta Math., 29(1979) 195-206.
  • L. A. Rubel and C. C. Yang, Values shared by an entire function and its derivative, Com- plex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976), Lecture Notes in Math., (1977), 101-103, Springer, Berlin.
  • L. Z. Yang, Solution of a diğ erential equation and its applications, Kodai Math. J., 22(1999), 464.
  • H. X. Yi, On characteristic function of a meromorphic function and its derivative, Indian J. Math., 33(2)(1991), 119-133.
  • Q. C. Zhang, The uniqueness of meromorphic functions with their derivatives, Kodai Math. J., 21(1998), 179-184.
  • Q. C. Zhang, Meromorphic function that shares one small function with its derivative. J. Inequal. Pure Appl. Math., 6(4)(2005), Art.116 [ ONLINE http://jipam.vu.edu.au/].
  • T. D. Zhang and W.R. Lü, Notes on meromorphic function sharing one small function with its derivative, Complex Var. Ellip. Eqn., 53(9)(2008), 857-867.
  • Current address : Department of Mathematics, University of Kalyani, West Bengal 741235, India.
Year 2016, Volume: 65 Issue: 1, 71 - 86, 01.02.2016
https://doi.org/10.1501/Commua1_0000000745

Abstract

References

  • T. C. Alzahary and H. X. Yi, Weighted value sharing and a question of I.Lahiri, Complex Var. Theory Appl., 49(15) (2004), 1063-1078.
  • A. Banerjee, Meromorphic functions sharing one value, Int. J. Math. Math. Sci., 22(2005), 3598.
  • R. Brück, On entire functions which share one value CM with their …rst derivative, Results Math., 30(1996), 21-24.
  • C. T. Chuang, On diğ erential polynomials, Analysis of one complex variable, (Laramie, Wyo., ), 12-32, World Sci. Publishing Singapore, (1987).
  • W. Doeringer, Exceptional values of diğ erential polynomials, Paci…c J. Math., 98(1)(1982), 62.
  • G. G. Gundersen and L. Z. Yang, Entire functions that share one value with one or two of their derivatives, J. Math. Anal. Appl., 223(1)(1998), 88-95.
  • W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, (1964).
  • I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., (2001), 193-206.
  • I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46(2001), 241-253.
  • I. Lahiri and A. Banerjee, Weighted sharing of two sets, Kyungpook Math. J., 46(1)(2006), 87.
  • I. Lahiri and S. Dewan, Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J., (2003), 95-100.
  • I. Lahiri and A. Sarkar, Uniqueness of meromorphic function and its derivative, J. Inequal. Pure Appl. Math., 5(1)(2004), Art.20 [ONLINE http://jipam.vu.edu.au/].
  • L. Liu, Uniqueness of meromorphic functions that share one small function with their deriv- atives, J.Math. Sci. : Adv. Appl., 6(2)(2010), 241-255.
  • N. Li and L. Z. Yang, Meromorphic function that shares one small function with its diğ er- ential polynomial, Kyungpook Math. J., 50(2010), 447-454.
  • A. Z. Mohon’ko, On the Nevanlinna characteristics of some meromorphic functions, Theory of Functions, Functional Analysis and Their Applications, 14(1971), 83-87.
  • E. Mues and N. Steinmetz, Meromorphe funktionen die unit ihrer ableitung werte teilen, Manuscripta Math., 29(1979) 195-206.
  • L. A. Rubel and C. C. Yang, Values shared by an entire function and its derivative, Com- plex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976), Lecture Notes in Math., (1977), 101-103, Springer, Berlin.
  • L. Z. Yang, Solution of a diğ erential equation and its applications, Kodai Math. J., 22(1999), 464.
  • H. X. Yi, On characteristic function of a meromorphic function and its derivative, Indian J. Math., 33(2)(1991), 119-133.
  • Q. C. Zhang, The uniqueness of meromorphic functions with their derivatives, Kodai Math. J., 21(1998), 179-184.
  • Q. C. Zhang, Meromorphic function that shares one small function with its derivative. J. Inequal. Pure Appl. Math., 6(4)(2005), Art.116 [ ONLINE http://jipam.vu.edu.au/].
  • T. D. Zhang and W.R. Lü, Notes on meromorphic function sharing one small function with its derivative, Complex Var. Ellip. Eqn., 53(9)(2008), 857-867.
  • Current address : Department of Mathematics, University of Kalyani, West Bengal 741235, India.
There are 23 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Abhijit Banerjee This is me

Sanjay Mallıck This is me

Publication Date February 1, 2016
Published in Issue Year 2016 Volume: 65 Issue: 1

Cite

APA Banerjee, A., & Mallıck, S. (2016). ABHIJIT BANERJEE AND SANJAY MALLICK. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 65(1), 71-86. https://doi.org/10.1501/Commua1_0000000745
AMA Banerjee A, Mallıck S. ABHIJIT BANERJEE AND SANJAY MALLICK. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2016;65(1):71-86. doi:10.1501/Commua1_0000000745
Chicago Banerjee, Abhijit, and Sanjay Mallıck. “ABHIJIT BANERJEE AND SANJAY MALLICK”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65, no. 1 (February 2016): 71-86. https://doi.org/10.1501/Commua1_0000000745.
EndNote Banerjee A, Mallıck S (February 1, 2016) ABHIJIT BANERJEE AND SANJAY MALLICK. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65 1 71–86.
IEEE A. Banerjee and S. Mallıck, “ABHIJIT BANERJEE AND SANJAY MALLICK”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 65, no. 1, pp. 71–86, 2016, doi: 10.1501/Commua1_0000000745.
ISNAD Banerjee, Abhijit - Mallıck, Sanjay. “ABHIJIT BANERJEE AND SANJAY MALLICK”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65/1 (February 2016), 71-86. https://doi.org/10.1501/Commua1_0000000745.
JAMA Banerjee A, Mallıck S. ABHIJIT BANERJEE AND SANJAY MALLICK. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65:71–86.
MLA Banerjee, Abhijit and Sanjay Mallıck. “ABHIJIT BANERJEE AND SANJAY MALLICK”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 65, no. 1, 2016, pp. 71-86, doi:10.1501/Commua1_0000000745.
Vancouver Banerjee A, Mallıck S. ABHIJIT BANERJEE AND SANJAY MALLICK. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65(1):71-86.

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