Generalization of value distribution and uniqueness of certain types of difference polynomials

Open access

Abstract

In this paper, we investigate the distribution of zeros as well as the uniqueness problems of certain type of differential polynomials sharing a small function with finite weight. The result obtained improves and generalizes the recent results.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] A. Banerjee Meromorphic functions sharing one value Int. J. Math. Math. Sci. 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. 2(2013) 124-136.

  • [3] M. R. Chen and Z. X. Chen Properties of difference polynomials of entire functions with Finite order Chinese Ann. Math. Ser. A 33(2012) 359-374.

  • [4] Y. M. Chiang and S. J. Feng On the Nevanlinna characteristic of f(z + ɳ) and difference equations in the complex plane Ramanujan J. 16(2008) 105-129.

  • [5] M. L. Fang and W. Hong A unicity theorem for entire functions concerning dif ferential poly- nomials Indian J. Pure Appl. Math. 32(2001) 1343-1348.

  • [6] M. L. Fang and X. H. Hua Entire functions that share one value J. Nanjing Univ. Math. Biquarterly 13(1996) 44-48.

  • [7] R. G. Halburd and R. J. Korhonen Nevanlinna theory for the difference operator Ann. Acad. Sci. Fenn. Math. 31(2006) 463-478.

  • [8] R. G. Halburd and R. J. Korhonen Difference analogue of the lemma on the logarithmic deriva- tive with application to difference equations J. Math. Anal. Appl. 314(2006) 477-487.

  • [9] W. K. Hayman Meromorphic Functions. Oxford Mathematical Monographs Clarendon Press Oxford 1964.

  • [10] I. Lahiri Weighted value sharing and uniqueness of meromorphic functions Complex Var. Theory Appl. 46(2001) 241-253.

  • [11] I. Laine Nevanlinna Theory and Complex Differential Equations Walter de Gruyter Berlin/Newyork 1993.

  • [12] I. Laine and C. C. Yang Value distribution of difference polynomials Proc. Japan Acad. SerA Math. Sci. 83(2007) 148-151.

  • [13] X. Luo and W. C. Lin Value sharing results for shifts of meromorphic functions J. Math. Anal. Appl. 377(2011) 441-449.

  • [14] X. G. Qi L. Z. Yang and K. Liu Uniqueness and periodicity of meromorphic functions con- cerning the difference operator Comput. Math. Appl. 60(2010) 1739-1746.

  • [15] P. Sahoo Uniqueness and weighted sharing of entire functions Kyungpook Math. J.51(2011) 145-164.

  • [16] P. Sahoo Entire functions that share fixed points with nite weights Bull. Belgian Math. Soc.-Simon Stevin 18(2011) 883-895.

  • [17] C. C. Yang and X. H. Hua Uniqueness and value sharing of meromorphic functions Ann. Acad. Sci. Fenn. Math. 22(1997) 395-406.

  • [18] H. X. Yi and C. C. Yang Uniqueness Theory of Meromorphic Functions Science Press Beijing 1995.

  • [19] J. L. Zhang Value distribution and shared sets of differences of meromorphic functions J. Math. Anal. Appl. 367(2010) 401-408.

  • [20] J. L. Zhang and L. Z. Yang Some results related to a conjecture of R. Bruck J. Inequal. Pure Appl. Math. 8(2007) Art. 18.

  • [21] P. Sahoo and B. Saha Value distribution and uniqueness of certain type of difference polyno- mials App. Math. E-Notes 16(2016) 33-34.

  • [22] P. Sahoo and S. Seikh Meromorphic functions whose certain differential polynomials share a small function with finite weight Analysis(Munich) 33(2013) 143-157.

  • [23] W.C. Lin and H.X. Yi Uniqueness theorems for meromorphic functions concerning fixed points Complex Var. Theory Appl. 49(2004) 793-806.

  • [24] H.Y. Xu T.B. Cao and S. Liu Uniqueness of meromorphic functions whose nonlinear differ- ential polynomials have one nonzero pseudo value Mat.Vesnik 64(2012) 1-16.

  • [25] H. Y. Xu C. F. Yi and T.B. Cao Uniqueness of meromorphic functions and differential polynomials sharing one value with finite weight Ann. Polon. Math 95(2009) 55-66.

  • [26] I. Lahiri Value distribution of certain differential polynomials Int. J. Math. Math. Sci. 28(2001) 83-91.

Search
Journal information
Impact Factor


Mathematical Citation Quotient (MCQ) 2017: 0.11

Target audience:

researchers in all areas of mathematics

Metrics
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 485 146 5
PDF Downloads 271 75 5