Unicity of Entire Functions Concerning Their Shifts and Derivatives

被引：5

作者：

Huang, Xiaohuang ^{[1
]}

Fang, Mingliang ^{[1
]}

机构：

[1] Hangzhou Dianzi Univ, Dept Math, Hangzhou 310012, Peoples R China

来源：

COMPUTATIONAL METHODS AND FUNCTION THEORY | 2021年 / 21卷 / 03期

关键词：

Unicity; Entire functions; Shifts; Derivatives;

D O I：

10.1007/s40315-020-00358-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the unicity of entire functions concerning their shifts and derivatives and prove: Let f be a non-constant entire function of hyper-order less than 1, let c be a non-zero finite value, and let a, b be two distinct finite values. If f '(z) and f(z+c) share a, b IM, then f '(z) equivalent to f(z+c). This improves some results due to Qi and Yang (Comput Methods Funct Theory 20:159-178, 2020).

引用

页码：523 / 532

页数：10

共 20 条

[1] NON-ARCHIMEDIAN ANALYTIC FUNCTIONS TAKING SAME VALUES AT SAME POINTS [J].

ADAMS, WW ;

STRAUS, EG .

ILLINOIS JOURNAL OF MATHEMATICS, 1971, 15 (03) :418-&

[2] Zeros of differences of meromorphic functions [J].

Bergweiler, Walter .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2007, 142 :133-147

[3] On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane [J].

Chiang, Yik-Man ;

Feng, Shao-Ji .

RAMANUJAN JOURNAL, 2008, 16 (01) :105-129

[4] ON THE GROWTH OF LOGARITHMIC DIFFERENCES, DIFFERENCE QUOTIENTS AND LOGARITHMIC DERIVATIVES OF MEROMORPHIC FUNCTIONS [J].

Chiang, Yik-Man ;

Feng, Shao-Ji .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 361 (07) :3767-3791

[5]

Halburd RG, 2006, ANN ACAD SCI FENN-M, V31, P463

[6] Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations [J].

Halburd, RG ;

Korhonen, RJ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 314 (02) :477-487

[7] HOLOMORPHIC CURVES WITH SHIFT-INVARIANT HYPERPLANE PREIMAGES [J].

Halburd, Rodney ;

Korhonen, Risto ;

Tohge, Kazuya .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 366 (08) :4267-4298

[8]

Hayman WK., 1964, MEROMORPHIC FUNCTION

[9] Uniqueness of meromorphic functions sharing values with their shifts [J].

Heittokangas, J. ;

Korhonen, R. ;

Laine, I. ;

Rieppo, J. .

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2011, 56 (1-4) :81-92

[10] EXISTENCE OF ZERO-ORDER MEROMORPHIC SOLUTIONS IN DETECTING q-DIFFERENCE PAINLEVE EQUATIONS [J].

Korhonen, Risto ;

Wen, Zhi-Tao .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 368 (07) :4993-5008

← 1 2 →