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Results on Certain Non-Linear Differential Polynomials Sharing a Small Function

Year 2014, Volume: 5 , 17 - 34, 06.03.2015

Abstract

In the paper we shall mainly concern about the special types of non-linear dierential polynomial as introduced in [20] sharing a small function. Our main result will improve, extend, unify and generalize a number of recent results.

References

  • A. Banerjee and P. Bhattacharjee, Some uniqueness results related to certain nonlinear dierential poly-
  • nomials sharing the same 1-points, Vietnam J. Math., 37 (2009), 97112.598.
  • A.Banerjee, On uniqueness for non-linear dierential polynomials sharing the same 1-points, Ann. Polon.
  • Math. 89(3) (2006), 259-272.
  • A.Banerjee, A uniqueness result on some dierential polynomials sharing 1 points, Hiroshima Math. J.
  • (3) 2007, 397-408.
  • A.Banerjee and P.Sahoo, Uniqueness of meromorphic functions when two dierential polynomials share
  • one value, Sarajevo.J. Math., 20(2012), 69-89
  • M.L.Fang and W. Hong, A unicity theorem for entire functions concerning dierential polynomials, Indian
  • J. Pure Appl. Math., 32(9) (2001), 1343-1348.
  • W.K.Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).
  • I.Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161 (2001), 193-
  • -
  • I.Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl.,
  • (2001), 241-253.
  • I. Lahiri and A. Banerjee, Weighted sharing of two sets, Kyungpook Math. J. Vol. 46 (2006) no. 1, pp.
  • -87.
  • I. Lahiri and S. Dewan, Value distribution of the product of a meromorphic function and its derivative,
  • Kodai Math. J., 26(1) (2003), 95-100.
  • I.Lahiri and N.Mandal, Uniqueness of nonlinear dierential polynomials sharing simple and double 1-
  • points, Int. J. Math. Math. Sci. 12 (2005), 1933-1942.
  • I.Lahiri and R.Pal, Nonlinear dierential polynomials sharing 1-points, Bull. Korean Math. Soc., 43(1)
  • (2006), 161-168.
  • I.Lahiri and A.Sarkar, Nonlinear dierential polynomials sharing 1-points with weight two, Chinese J.
  • Contemp. Math., 25(3) (2004), 325-334.
  • I.Lahiri and P.Sahoo, Uniqueness of non-linear dierential polynomials sharing 1-points, Georgian Math.
  • J., 12(1) (2005), 131-138.
  • W.C.Lin, Uniqueness of dierential polynomials and a question of Lahiri, Pure Appl. Math., 17(2)(2001),
  • -110 (in Chinese).
  • W.C.Lin and H.X.Yi, Uniqueness theorems for meromorphic function, Indian J. Pure Appl. Math.,
  • (2)(2004), 121-132.
  • C. Meng, On unicity of meromorphic functions when two dierential polynomials share one value, Hi-
  • roshima Math. J., 39(2009), 163-169.
  • C. Meng, Uniqueness for meromorphic functions concerning dierential polynomials, Georgian Math. J.,
  • (4)(2008), 731-738.
  • P. Sahoo and S. Seikh, Meromorphic functions whose certain dierential polynomials share a small
  • function with nite weight, Math. Vesnik., 65(2), (2013), 151-165.
  • S.H.Shen and W.C.Lin, Uniqueness of meromorphic functions, Complex Var. Elliptic Equ., 52(5)(2007),
  • -424.
  • W. L. Xiong, W. C. Lin and S. Mori, Uniqueness of meromorphic functions, Sci. Math. Jpn., 62(2) (2005),
  • -315.
  • C.C.Yang and X.H.Hua, Uniqueness and value sharing of meromorphic functions,
  • Ann.Acad.Sci.Fenn.Math. 22(1997), 395-406.
  • H.X.Yi, On characteristic function of a meromorphic function and its derivative, Indian J. Math.
  • (2)(1991), 119-133.
  • H. X. Yi, C. C. Yang, Uniqueness Theory of meromorphic functions, Science Press, Beijing, 1995.
  • K.Yamanoi, The second main theorem for small functions and related problems, Acta Math. 192(2004),
  • -294.
  • X. Y. Zhang, J. F. Chen and W.C. Lin, Entire or meromorphic functions sharing one value, Comput.
  • Math. Appl. 56 (2008), 18761883.
  • X. B. Zhang and J. F. Xu, Uniqueness of meromorphic functions sharing a small function and its
  • applications, Comput. Math. Appl, 61(2011), 722-730.
  • 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/].
Year 2014, Volume: 5 , 17 - 34, 06.03.2015

Abstract

References

  • A. Banerjee and P. Bhattacharjee, Some uniqueness results related to certain nonlinear dierential poly-
  • nomials sharing the same 1-points, Vietnam J. Math., 37 (2009), 97112.598.
  • A.Banerjee, On uniqueness for non-linear dierential polynomials sharing the same 1-points, Ann. Polon.
  • Math. 89(3) (2006), 259-272.
  • A.Banerjee, A uniqueness result on some dierential polynomials sharing 1 points, Hiroshima Math. J.
  • (3) 2007, 397-408.
  • A.Banerjee and P.Sahoo, Uniqueness of meromorphic functions when two dierential polynomials share
  • one value, Sarajevo.J. Math., 20(2012), 69-89
  • M.L.Fang and W. Hong, A unicity theorem for entire functions concerning dierential polynomials, Indian
  • J. Pure Appl. Math., 32(9) (2001), 1343-1348.
  • W.K.Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).
  • I.Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161 (2001), 193-
  • -
  • I.Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl.,
  • (2001), 241-253.
  • I. Lahiri and A. Banerjee, Weighted sharing of two sets, Kyungpook Math. J. Vol. 46 (2006) no. 1, pp.
  • -87.
  • I. Lahiri and S. Dewan, Value distribution of the product of a meromorphic function and its derivative,
  • Kodai Math. J., 26(1) (2003), 95-100.
  • I.Lahiri and N.Mandal, Uniqueness of nonlinear dierential polynomials sharing simple and double 1-
  • points, Int. J. Math. Math. Sci. 12 (2005), 1933-1942.
  • I.Lahiri and R.Pal, Nonlinear dierential polynomials sharing 1-points, Bull. Korean Math. Soc., 43(1)
  • (2006), 161-168.
  • I.Lahiri and A.Sarkar, Nonlinear dierential polynomials sharing 1-points with weight two, Chinese J.
  • Contemp. Math., 25(3) (2004), 325-334.
  • I.Lahiri and P.Sahoo, Uniqueness of non-linear dierential polynomials sharing 1-points, Georgian Math.
  • J., 12(1) (2005), 131-138.
  • W.C.Lin, Uniqueness of dierential polynomials and a question of Lahiri, Pure Appl. Math., 17(2)(2001),
  • -110 (in Chinese).
  • W.C.Lin and H.X.Yi, Uniqueness theorems for meromorphic function, Indian J. Pure Appl. Math.,
  • (2)(2004), 121-132.
  • C. Meng, On unicity of meromorphic functions when two dierential polynomials share one value, Hi-
  • roshima Math. J., 39(2009), 163-169.
  • C. Meng, Uniqueness for meromorphic functions concerning dierential polynomials, Georgian Math. J.,
  • (4)(2008), 731-738.
  • P. Sahoo and S. Seikh, Meromorphic functions whose certain dierential polynomials share a small
  • function with nite weight, Math. Vesnik., 65(2), (2013), 151-165.
  • S.H.Shen and W.C.Lin, Uniqueness of meromorphic functions, Complex Var. Elliptic Equ., 52(5)(2007),
  • -424.
  • W. L. Xiong, W. C. Lin and S. Mori, Uniqueness of meromorphic functions, Sci. Math. Jpn., 62(2) (2005),
  • -315.
  • C.C.Yang and X.H.Hua, Uniqueness and value sharing of meromorphic functions,
  • Ann.Acad.Sci.Fenn.Math. 22(1997), 395-406.
  • H.X.Yi, On characteristic function of a meromorphic function and its derivative, Indian J. Math.
  • (2)(1991), 119-133.
  • H. X. Yi, C. C. Yang, Uniqueness Theory of meromorphic functions, Science Press, Beijing, 1995.
  • K.Yamanoi, The second main theorem for small functions and related problems, Acta Math. 192(2004),
  • -294.
  • X. Y. Zhang, J. F. Chen and W.C. Lin, Entire or meromorphic functions sharing one value, Comput.
  • Math. Appl. 56 (2008), 18761883.
  • X. B. Zhang and J. F. Xu, Uniqueness of meromorphic functions sharing a small function and its
  • applications, Comput. Math. Appl, 61(2011), 722-730.
  • 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/].
There are 54 citations in total.

Details

Primary Language English
Journal Section Mathematics
Authors

Abhijit Banerjee

Molla Ahamed This is me

Publication Date March 6, 2015
Published in Issue Year 2014 Volume: 5

Cite

APA Banerjee, A., & Ahamed, M. (2015). Results on Certain Non-Linear Differential Polynomials Sharing a Small Function. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy, 5, 17-34.
AMA Banerjee A, Ahamed M. Results on Certain Non-Linear Differential Polynomials Sharing a Small Function. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy. March 2015;5:17-34.
Chicago Banerjee, Abhijit, and Molla Ahamed. “Results on Certain Non-Linear Differential Polynomials Sharing a Small Function”. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy 5, March (March 2015): 17-34.
EndNote Banerjee A, Ahamed M (March 1, 2015) Results on Certain Non-Linear Differential Polynomials Sharing a Small Function. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy 5 17–34.
IEEE A. Banerjee and M. Ahamed, “Results on Certain Non-Linear Differential Polynomials Sharing a Small Function”, İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy, vol. 5, pp. 17–34, 2015.
ISNAD Banerjee, Abhijit - Ahamed, Molla. “Results on Certain Non-Linear Differential Polynomials Sharing a Small Function”. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy 5 (March 2015), 17-34.
JAMA Banerjee A, Ahamed M. Results on Certain Non-Linear Differential Polynomials Sharing a Small Function. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy. 2015;5:17–34.
MLA Banerjee, Abhijit and Molla Ahamed. “Results on Certain Non-Linear Differential Polynomials Sharing a Small Function”. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy, vol. 5, 2015, pp. 17-34.
Vancouver Banerjee A, Ahamed M. Results on Certain Non-Linear Differential Polynomials Sharing a Small Function. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy. 2015;5:17-34.