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On Uniqueness of Meromorphic Functions Partially Sharing Values with Their q-shifts

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Abstract

In this work, we give some uniqueness theorems for non-constant zero-order meromorphic functions when they and their q-shifts partially share values in the extended complex plane. This is a continuation of previous works of Charak et al. (J Math Anal Appl 435(2):1241–1248, 2016) and of Lin et al. (Bull Korean Math Soc 55(2):469–478, 2018). Furthermore, we show some uniqueness results in the case multiplicities of partially shared values are truncated to level \(m\ge 4\). As a consequence, we obtain a uniqueness result for an entire function of zero-order if it and its q-shift partially share three distinct values \(a_1, a_2, a_3\) without truncated multiplicities, in which we do not need to count \(a_j\)-points of multiplicities greater than 38 for all \(j=1,2,3\).

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Acknowledgements

The authors wish to express their thanks to the referee for his/her valuable suggestions and comments which helped us improve our paper. This research is funded by National University of Civil Engineering (NUCE) under grant number 22-2019/KHXD-T Ɖ.

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Authors and Affiliations

  1. Department of Mathematics, National University of Civil Engineering, 55 Giai Phong Str., Hanoi, Vietnam

    Pham Duc Thoan & Luong Thi Tuyet

  2. Department of Mathematics, Hanoi National University of Education, 136-Xuan Thuy Str., Hanoi, Vietnam

    Noulorvang Vangty

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  1. Pham Duc Thoan
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  2. Luong Thi Tuyet
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  3. Noulorvang Vangty
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Correspondence to Noulorvang Vangty.

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Communicated by Ilpo Laine.

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Thoan, P.D., Tuyet, L.T. & Vangty, N. On Uniqueness of Meromorphic Functions Partially Sharing Values with Their q-shifts. Comput. Methods Funct. Theory 21, 361–378 (2021). https://doi.org/10.1007/s40315-020-00354-5

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