The Journal of the Indian Mathematical Society

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Uniqueness for Q-shift of Meromorphic Functions of Zero Order Sharing Small Function


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1 Department of Mathematics, India
     

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To study the uniqueness results for q-shift differential-difference polynomials of meromorphic functions of zero order sharing a small function, we consider the problems in [12] and [8]. We point out a number of gaps in its main proof and rectify these. Then present an improved as well as generalized result in a more compact form. Also, exhibit some examples to show that one of the conditions of the obtained result is best possible.

Keywords

Meromorphic Function, Uniqueness, q-shift, Zero Order.
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  • A. Banerjee, Uniqueness of meromorphic functions sharing two sets with finite weight, Port. Math. (N. S), 65 (2008), 81-93.

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

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

  • W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).

  • I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161(2001), 193-206.

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

  • I. Laine and C. C. Yang, Value distribution of difference polynomials, Proc. Japan Acad. Ser. A, 83 (2007), 148-151.

  • M. Lin, W. Lin and J. Luo, Uniqueness of q-shift difference-differential polynomials of entire functions, Palestine J. Math., 5 (2) (2016), 104-116.

  • K. Liu and X. G. Qi, Meromorphic solutions of q-shift difference equations, Ann. Polon. Math., 101 (2011), 215-225.

  • K. Liu and L. Z. Yang, Value distribution of the difference operator, Arch. Math., 92 (2009), 270-278.

  • P. Sahoo, Meromorphic functions that share fixed points with finite weights, Bull. Math. Anal. Appl., 2 (2010), 106-118.

  • P. Sahoo and G. Biswas, Value distribution and uniqueness of q-shift difference polynomials, Novi Sad J. Math., 46 (2) (2016), 33-44.

  • H. Y. Xu, K. Liu and T. B. Cao, Uniqueness and Value distribution for q-shifts of meromorphic functions, Math. Commun., 20 (2015), 97-112.

  • C. C. Yang, On deficiencies of differential polynomials II, Math. Z., 125 (1972), 107-112.

  • K. Yamanoi, The second main theorem for small functions and related problems, Acta Math., 192 (2004) 225-294.

  • J. L. Zhang and R. J. Korhonen, On the Nevanlinna characteristic of f(qz) and its application, J. Math. Anal. Appl., 369 (2010), 537-544.

  • Q. C. Zhang, Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl. Math., 6 (4)(2005), Art. 116.


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  • Uniqueness for Q-shift of Meromorphic Functions of Zero Order Sharing Small Function

Abstract Views: 277  |  PDF Views: 1

Authors

Rajib Mandal
Department of Mathematics, India

Abstract


To study the uniqueness results for q-shift differential-difference polynomials of meromorphic functions of zero order sharing a small function, we consider the problems in [12] and [8]. We point out a number of gaps in its main proof and rectify these. Then present an improved as well as generalized result in a more compact form. Also, exhibit some examples to show that one of the conditions of the obtained result is best possible.

Keywords


Meromorphic Function, Uniqueness, q-shift, Zero Order.

References