Uniqueness of Meromorphic Functions Sharing Values with their nth Order Exact Differences

Z. Gao; R. Korhonen; J. Zhang; Y. Zhang

doi:10.1007/s10476-018-0605-2

Uniqueness of Meromorphic Functions Sharing Values with their nth Order Exact Differences

Z. Gao
, R. Korhonen^*
, J. Zhang
, Y. Zhang

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

Let f(z) be a transcendental meromorphic function in the complex plane of hyper-order strictly less than 1. It is shown that if f(z) and its nth exact difference Δⁿf(z) (≢ 0) share three distinct periodic functions a,b,c∈S^(f) with period 1 CM, where S^(f)=S(f)∪{∞} and S(f) denotes the set of all small functions of f(z), then Δⁿf(z) ≡ f(z).

Original language	English
Pages (from-to)	321-334
Number of pages	14
Journal	Analysis Mathematica
Volume	45
Issue number	2
DOIs	https://doi.org/10.1007/s10476-018-0605-2
State	Published - 1 Jun 2019

Keywords

exact difference
meromorphic function
sharing values
uniqueness

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title = "Uniqueness of Meromorphic Functions Sharing Values with their nth Order Exact Differences",

abstract = "Let f(z) be a transcendental meromorphic function in the complex plane of hyper-order strictly less than 1. It is shown that if f(z) and its nth exact difference Δnf(z) (≢ 0) share three distinct periodic functions a,b,c∈S\textasciicircum{}(f) with period 1 CM, where S\textasciicircum{}(f)=S(f)∪\{∞\} and S(f) denotes the set of all small functions of f(z), then Δnf(z) ≡ f(z).",

keywords = "exact difference, meromorphic function, sharing values, uniqueness",

author = "Z. Gao and R. Korhonen and J. Zhang and Y. Zhang",

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T1 - Uniqueness of Meromorphic Functions Sharing Values with their nth Order Exact Differences

AU - Gao, Z.

AU - Korhonen, R.

AU - Zhang, J.

AU - Zhang, Y.

PY - 2019/6/1

Y1 - 2019/6/1

N2 - Let f(z) be a transcendental meromorphic function in the complex plane of hyper-order strictly less than 1. It is shown that if f(z) and its nth exact difference Δnf(z) (≢ 0) share three distinct periodic functions a,b,c∈S^(f) with period 1 CM, where S^(f)=S(f)∪{∞} and S(f) denotes the set of all small functions of f(z), then Δnf(z) ≡ f(z).

AB - Let f(z) be a transcendental meromorphic function in the complex plane of hyper-order strictly less than 1. It is shown that if f(z) and its nth exact difference Δnf(z) (≢ 0) share three distinct periodic functions a,b,c∈S^(f) with period 1 CM, where S^(f)=S(f)∪{∞} and S(f) denotes the set of all small functions of f(z), then Δnf(z) ≡ f(z).

KW - exact difference

KW - meromorphic function

KW - sharing values

KW - uniqueness

UR - https://www.scopus.com/pages/publications/85055489907

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M3 - 文章

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VL - 45

SP - 321

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JO - Analysis Mathematica

JF - Analysis Mathematica

IS - 2

ER -

Uniqueness of Meromorphic Functions Sharing Values with their nth Order Exact Differences

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Keywords

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