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<p>In this paper, we provide a general characterisation of unique range sets for meromorphic functions over a non-Archimedean field under relaxed sharing hypothesis which extends, generalizes and improves all the existing results in this direction. In addition, in Section-5, by exhibiting a number of examples, for the first time in the literature, we confirm that our results also hold for non-critically injective polynomials as well as polynomials which are still not determined to be critically injective or non-critically injective.</p>

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On the General Structure of Unique Range Sets over a Non-Archimedean Field

  • 期刊论文

  • 发表日期：

    2025年3月28日

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  • Sanjay Mallick

摘要

In this paper, we provide a general characterisation of unique range sets for meromorphic functions over a non-Archimedean field under relaxed sharing hypothesis which extends, generalizes and improves all the existing results in this direction. In addition, in Section-5, by exhibiting a number of examples, for the first time in the literature, we confirm that our results also hold for non-critically injective polynomials as well as polynomials which are still not determined to be critically injective or non-critically injective.