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On Homogeneous differential polynomials of Meromorphic Functions

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Acta Mathematica Sinica,English Series 2005年第2期21卷 261-266页

作者： WeiChuanLIN HongXunYI DepartmentofMathematics ShantouUniversityShantou515063P.R.China//DepartmentofMathematicsFujianTeachersUniversityFuzhou350007P.R.China DepartmentofMathematics ShandongUniversityJinan250100P.R.China

In this paper, we study one conjecture proposed by W. Bergweiler and showthat any transcendental meromorphic functions f(z) have the form exp(αz + β) if f(z)f″(z) —a(f′(z))~2 7≠ 0, where a ≠ 1, (n±1)/n, n ∈ N... 详细信息

关键词： differential polynomial normal family meromorphic function

FIXED POINTS OF THE lTH POWER OF differential polynomialS GENERATED BY SOLUTIONS OF differential EQUATIONS

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Journal of Systems Science & Complexity 2004年第2期17卷 271-280页

作者： WANGJun YIHongxun CAIHuiping InstituteofMathematics FudanUniversityShanghai200433China DepartmentofMathematics ShandongUniversityJinan250100China DepartmentofMathematics ShijiazhuangTeachersCollegeShijiazhuang050801China

In this paper,we study the problem on the fixed points of the lth power of linear differential polynomials generated by second order linear differential *** of the control of differential equation,we can obtain some p... 详细信息

关键词： second order differential equation fixed point differential polynomial order hyper-order

Shared Values of Certain Nonlinear differential polynomials of Meromorphic Functions

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Communications in Mathematical Research 2017年第4期33卷 347-358页

作者： CHEN JUN-FAN CAI XIAO-HUA Ji You-qing Department of Mathematics Fujian Normal University

In this paper, by using the idea of truncated counting functions of meromorphic functions, we deal with the problem of uniqueness of the meromorphic functions whose certain nonlinear differential polynomials share one... 详细信息

关键词： meromorphic function shared value differential polynomial uniqueness

Notes on Zeros of differential polynomials

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Northeastern Mathematical Journal 2007年第2期23卷 95-102页

作者：吕巍然王赞春仪洪勋 Department of Mathematics University of Petroleum Dongying 257061 Department of Mathematics Shandong University Jinan 250100

The value distribution of differential polynomials is studied. The results in this paper improve and generalize some previous theorems given by Yang Chungchun （On deficiencies of differential polynomials, Math. Z., 116（1970）, 197- 204）, H. S. Gopalakrishna and S. S. Bhoosnurmath （On distribution of values of differential polynomials, Indian 3. Pure Appl. Math., 17（1986）, 367-372）, I. Lahiri （A note on distribution of nonhomogeneous differential polynomials, Hokkaido Math. J., 31（2002）, 453-458） and Yi Hongxun （On zeros of differential polynomials, Adv. in Math., 18（1989）, 335-351） et al. Examples show that the results in this paper are sharu.

关键词： meromorphic function zero-point differential polynomial

NORMALITY AND THE NUMBER OF ZEROS

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数学杂志 2024年第5期44卷 377-382页

作者： WANG Guang-sheng WEI Dong-mei XU Yan School of Mathematics and Physics Nanjing Institute of TechnologyNanjing 211167China School of Mathematics Nanjing Normal UniversityNanjing 210023China

In this paper,we study normal families of meromorphic *** using the idea in[11],we obtain some normality criteria for families of meromorphic functions that concern the number of zeros of the differential polynomial,which extends the related result of Li,and Chen et al..An example is given to show that the hypothesis on the zeros of a(z)is necessary.

关键词： Meromorphic function normal family differential polynomial zero

NORMAL FAMILY OF MEROMORPHIC FUNCTIONS SHARING HOLOMORPHIC FUNCTIONS AND THE CONVERSE OF THE BLOCH PRINCIPLE

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Acta Mathematica Scientia 2017年第3期37卷 623-656页

作者： Nguyen Van THIN Department of Mathematics Thai Nguyen University of EducationLuong Ngoc Quyen StreetThai Nguyen cityThai NguyenViet Nam

In 1996, C. C. Yang and P. C. Hu [8] showed that： Let f be a transcendental meromorphic function on the complex plane, and a ≠ 0 be a complex number; then assume that n 〉 2, n1,… , nk are nonnegative integers such that n1＋… ＋ nk ≥1; thus fn（f′）n1…（f（k））nk-a has infinitely zeros. The aim of this article is to study the value distribution of differential polynomial, which is an extension of the result of Yang and Hu for small function and all zeros of f having multiplicity at least k ≥2. Namely, we prove that fn（f′）n1…（f（k））nk-a（z） has infinitely zeros, where f is a transcendental meromorphic function on the complex plane whose all zeros have multiplicity at least k≥ 2, and a（z） 0 is a small function of f and n ≥ 2, n1,… ,nk are nonnegative integers satisfying n1＋ …＋ nk ≥1. Using it, we establish some normality criterias for a family of meromorphic functions under a condition where differential polynomials generated by the members of the family share a holomorphic function with zero points. The results of this article are supplement of some problems studied by d. Yunbo and G. Zongsheng [6], and extension of some problems studied X. Wu and Y. Xu [10]. The main result of this article also leads to a counterexample to the converse of Bloeh＇s principle.

关键词： Normal family Nevanlinna theory meromorphic function sharing function differential polynomial

Entire Functions Sharing One Value with Finite Weight

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Journal of Mathematical Research and Exposition 2010年第4期30卷 687-695页

作者： Hong Yan XU Ting Bin CAO Department of Informatics and Engineering Jingdezhen Ceramic Institute Jiangxi 333403 P. R. China Department of Mathematics Nanchang University Jiangxi 330031 P. R. China

This paper deals with some uniqueness problems of entire functions concerning differential polynomials that share one value with finite weight in a different form. We obtain some theorems which generalize some results... 详细信息

关键词： entire functions differential polynomial weighted sharing.

ON VALUE DISTRIBUTIONS OF GENERAL differential MONOMIALS

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Transactions of Tianjin University 2001年第1期7卷 68-70页

作者：吴天毅李伟程英天津轻工业学院天津300222 菏泽师范专科学校山东菏泽274015

Value distributions of the general differential monomials is *** following theorem is obtained:Let f be a transcendental meromorphic function in the plane,F=f n 0 (f (i) ) n i …(f (k) ) n k -c,n i≥1,c≠0 be a constant then (n 0-2)T(r,f)≤(r,1F)+S(r,f) when n 0>2;T(r,f)≤7(i+1)i( i) (r,1f)+(r,1F))+S(r,f) when n 0=1;T(r,f)≤7(N(r,1f)+(r,1F))+S(r,f) when n 0=0.

关键词： meromorphic function differential monomial differential polynomial value distribution

On the value distribution of f^nf^(k)

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Journal of Chongqing University 2007年第4期6卷 302-304页

作者：黄小杰兰福祥 Department of Mathematics Chongqing University

This paper presents an inequality, by use of which some results about the value distribution of f nf (k) are proved, where n and k are two positive integers.

关键词： transcendental meromorphic function Nevanlinna theory differential polynomial