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On the Value Distribution of \({\varvec{f}}^{{\varvec{n}}} {\varvec{f}}^{({\varvec{k}})}-\mathbf 1 \)

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Abstract

In this paper, we consider the value distribution of the differential polynomial \(f^{n}f^{(k)}-1\) where \(n(\ge 2)\) and \(k(\ge 1)\) are integers and obtain some inequalities concerning the Nevanlinna characteristic function T(r, f). Our result improves and generalizes the results obtained by Xu et al. (Math Inequal Appl 14:93–100, 2011).

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Acknowledgements

The authors are grateful to the referee and editor for their valuable comments and suggestions towards the improvement of this paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Kalyani, Kalyani, West Bengal, 741235, India

    Himadri Karmakar & Pulak Sahoo

Authors
  1. Himadri Karmakar
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  2. Pulak Sahoo
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Corresponding author

Correspondence to Pulak Sahoo.

Additional information

The first author is thankful to UGC-JRF scheme and the second (corresponding) author is thankful to DST-PURSE programme for financial assistance.

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Karmakar, H., Sahoo, P. On the Value Distribution of \({\varvec{f}}^{{\varvec{n}}} {\varvec{f}}^{({\varvec{k}})}-\mathbf 1 \). Results Math 73, 98 (2018). https://doi.org/10.1007/s00025-018-0859-9

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  • DOI: https://doi.org/10.1007/s00025-018-0859-9

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