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Uniqueness of entire functions concerning differential–difference polynomials sharing small functions

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Abstract

In this paper, we investigate the uniqueness problem of differential–difference polynomials \((f^{n}(z)P(f)L_c(f))^{(k)}\) and \((g^{n}(z)P(g)L_c(g))^{(k)}\) sharing a small function under the notion of weakly weighted sharing and relaxed weighted sharing, where \(L_c(f)=f(z+c)+c_0f(z)\), P(z) is a polynomial with constant coefficients of degree m, and obtained the corresponding results, which improve and extend some recent results due to Sahoo and Biswas (Tamkang J. Math., 49, 85–97 (2018)). Some examples have been exhibited which are relevant to the content of the paper.

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Data Availability Statement

Data sharing is not applicable to this article as no database were generated or analyzed during the current study.

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Acknowledgements

The author would like to thank the referees for their helpful suggestions and remarks for improvement the work of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Malda College, Rabindra Avenue, Malda, West Bengal, 732101, India

    Goutam Haldar

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  1. Goutam Haldar
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Communicated by Samy Ponnusamy.

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Haldar, G. Uniqueness of entire functions concerning differential–difference polynomials sharing small functions. J Anal 30, 785–806 (2022). https://doi.org/10.1007/s41478-021-00373-y

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  • DOI: https://doi.org/10.1007/s41478-021-00373-y

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