Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Value Sharing Results for Generalized Shifts of Entire Functions


Affiliations
1 Department of Mathematics, Malda College, Malda - 732101 West Bengal, India
     

   Subscribe/Renew Journal


In this paper, we investigate the uniqueness problem of generalized shift polynomials of finite order entire functions sharing a small function under the notion of weakly and relaxed weighted sharing environment. Some examples have been exhibited which are relevant to the content of the paper.

Keywords

Meromorphic Function, Entire Function, Shift Operator, Small Function, Weakly Weighted Sharing, Relaxed Weighted Sharing.
Subscription Login to verify subscription
User
Notifications
Font Size


  • A. Banerjee and S. Mukherjee, Uniqueness of meromorphic functions concerning differential monomials sharing the same value, Bull. Math. Soc. Sci. Math. Roum. Nouv. Ser., 50 (2007), 191 – 206.
  • W. Bergweiler and J. K. Langley, Zeros of difference of meromorphic functions, Math. Proc. Camb. Philos Soc., 142 (2007), 133 – 147.
  • Y. M. Chiang and S. J. Feng, On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane, Ramanujan J., 16 (2008), 105 – 129.
  • C. Y. Fang and M. L. Fang, Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl., 44 (2002), 607 – 617.
  • R. G. Halburdand and R. J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math., 31(2) (2006), 463 – 478.
  • W. K. Hayman, Picard values of meromorphic Functions and their derivatives, Ann. Math., 70 (1959), 9 – 42.
  • W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964.
  • J. Heittokangas, J., R. Korhonen, I. Laine, J. Rieppo and J. L. Zhang, Value sharing results for shifts of meromorphic function, and sufficient conditions for periodicity, J. Math. Anal. Appl., 355 (2009), 352 – 363.
  • I. Lahiri, Value distribution of certain differential polynomials, Int. J. Math. Math. Sci., 28 (2001), 83 – 91.
  • I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46 (2001), 241 – 253.
  • S. H. Lin and W. C. Lin, Uniqueness of meromorphic functions concerning weakly weighted sharing, Kodai Math. J., 29 (2006), 269 – 280.
  • X. Q. Lin and W. C. Lin, Uniqueness of entire functions sharing one value, Acta Math. Sci., Ser. B. Engl. Ed., 31 (2011), 1062 – 1076.
  • X. Luo and W. C. Lin, Value sharing results for shifts of meromorphic functions, J. Math. Anal. Appl., 377 (2011), 441 – 449.
  • C. Meng, Uniqueness of entire functions concerning difference polynomials, Math. Bohem., 139 (2014), 89 – 97.
  • P. Sahoo, Uniqueness of Entire Functions Related to Difference Polynomials, Commun. Math. Stat., 3 (2015), 227 – 238.
  • C. C. Yang, On deficiencies of differential polynomials II, Math. Z., 125 (1972), 107 – 112.
  • 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, Meromorphic functions that share one or two values, Complex Var. Theory Appl., 28 (1995), 1 – 11.
  • J. L. Zhang, Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl., 367 (2010), 401 – 408.

Abstract Views: 232

PDF Views: 0




  • Value Sharing Results for Generalized Shifts of Entire Functions

Abstract Views: 232  |  PDF Views: 0

Authors

Goutam Haldar
Department of Mathematics, Malda College, Malda - 732101 West Bengal, India

Abstract


In this paper, we investigate the uniqueness problem of generalized shift polynomials of finite order entire functions sharing a small function under the notion of weakly and relaxed weighted sharing environment. Some examples have been exhibited which are relevant to the content of the paper.

Keywords


Meromorphic Function, Entire Function, Shift Operator, Small Function, Weakly Weighted Sharing, Relaxed Weighted Sharing.

References