Uniqueness of differential q-shift difference polynomials of entire functions

Abstract

In this paper, we prove the uniqueness theorems of differential q-shift difference polynomials of transcendental entire functions.

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References

  1. 1.

    Chen, H.H., Feng, M.L. 1995. On the value distribution of \(f^nf^{^{\prime }}\). Science in China Series-A 38: 789–798.

    MathSciNet  Google Scholar 

  2. 2.

    Chern, P.T.Y. 2006. On meromorphic functions with finite logarithmic order. Transactions of the American Mathematical Society 358 (2): 473–489.

    MathSciNet  Article  Google Scholar 

  3. 3.

    Hayman, W.K. 1964. Meromorphic Functions. Oxford: Clarendon Press.

    Google Scholar 

  4. 4.

    Liu, K., Qi, X.G. 2011. Meromorphic solutions of \(q-\)shift difference equations. Annales Polonici Mathematici 101: 215–225.

    MathSciNet  Article  Google Scholar 

  5. 5.

    Xu, J., Zhang, X. 2012. The zeros of q-shift difference polynomials of meromorphic functions. Advances in Difference Equations 200: 1–10.

    MathSciNet  MATH  Google Scholar 

  6. 6.

    Yang, L. 1993. Value Distribution Theory. Berlin: Springer.

    Google Scholar 

  7. 7.

    Yang, C.C., Yi, H. X 2003. Uniqueness Theory of Meromorphic functions. New York: Kluwer Academic Publishers.

    Google Scholar 

  8. 8.

    Zheng, X.M., Xu, H.Y. 2014. On value distribution and uniqueness of meromorphic function with finite logarithmic order concerning its derivative and \(q-\)shift difference. Journal of Inequalities and Applications 295: 1–11.

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

Authors are indebted to the editor and referees for their careful reading and valuable suggestions which helped to improve the manuscript

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Correspondence to Madhura M. Mathai.

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Communicated by Samy Ponnusamy.

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Mathai, M.M., Manjalapur, V.V. Uniqueness of differential q-shift difference polynomials of entire functions. J Anal (2021). https://doi.org/10.1007/s41478-020-00299-x

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Keywords

  • differential q-shift difference
  • logarithmic order
  • meromorphic function
  • Nevanlinna theory.

Mathematics Subject Classification

  • MSC 30D35
  • MSC 39A05