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CRITERIA OF NORMALITY CONCERNING THE SEQUENCE OF OMITTED FUNCTIONS
Chen, Qiaoyu,Qi, Jianming Korean Mathematical Society 2016 대한수학회보 Vol.53 No.5
In this paper, we research the normality of sequences of meromorphic functions concerning the sequence of omitted functions. The main result is listed below. Let {$f_n(z)$} be a sequence of functions meromorphic in D, the multiplicities of whose poles and zeros are no less than k + 2, $k{\in}\mathbb{N}$. Let {$b_n(z)$} be a sequence of functions meromorphic in D, the multiplicities of whose poles are no less than k + 1, such that $b_n(z)\overset{\chi}{\Rightarrow}b(z)$, where $b(z({\neq}0)$ is meromorphic in D. If $f^{(k)}_n(z){\neq}b_n(z)$, then {$f_n(z)$} is normal in D. And we give some examples to indicate that there are essential differences between the normal family concerning the sequence of omitted functions and the normal family concerning the omitted function. Moreover, the conditions in our paper are best possible.
Two meromorphic functions sharing sets concerning small functions
Ting-Bin Cao 대한수학회 2009 대한수학회보 Vol.46 No.6
The main purpose of this paper is to deal with the uniqueness of meromorphic functions sharing sets concerning small functions. We obtain two main theorems which improve and extend strongly some results due to R. Nevanlinna, Li-Qiao, Yao, Yi, Thai-Tan, and Cao-Yi. The main purpose of this paper is to deal with the uniqueness of meromorphic functions sharing sets concerning small functions. We obtain two main theorems which improve and extend strongly some results due to R. Nevanlinna, Li-Qiao, Yao, Yi, Thai-Tan, and Cao-Yi.
Criteria of normality concerning the sequence of omitted functions
Qiaoyu Chen,Jianming Qi 대한수학회 2016 대한수학회보 Vol.53 No.5
In this paper, we research the normality of sequences of meromorphic functions concerning the sequence of omitted functions. The main result is listed below. Let $\{f_{n}(z)\}$ be a sequence of functions meromorphic in $D$, the multiplicities of whose poles and zeros are no less than $k+2,~k\in \mathbb N$. Let $\{b_{n}(z)\}$ be a sequence of functions meromorphic in $D$, the multiplicities of whose poles are no less than $ k+1$, such that $b_{n}(z)\overset\chi\Rightarrow b(z)$, where $b(z)(\neq 0)$ is meromorphic in $D$. If $f^{(k)}_{n}(z)\ne b_{n}(z)$, then $\{f_{n}(z)\}$ is normal in $D$. And we give some examples to indicate that there are essential differences between the normal family concerning the sequence of omitted functions and the normal family concerning the omitted function. Moreover, the conditions in our paper are best possible.
Tanmay Biswas 한국수학교육학회 2019 純粹 및 應用數學 Vol.26 No.4
Orders and types of entire and meromorphic functions have been actively investigated by many authors. In the present paper, we aim at investigating some basic properties in connection with sum and product of relative (p,q)-ϕ order, relative (p,q)-ϕ type, and relative (p,q)-ϕ weak type of meromorphic functions with respect to entire functions where p,q are any two positive integers and ϕ : [0,+∞)→(0,+∞) be a non-decreasing unbounded function.
Value Sharing and Uniqueness for the Power of P-Adic Meromorphic Functions
CHAO MENG,Gang Liu,Liang Zhao 한국전산응용수학회 2018 Journal of applied mathematics & informatics Vol.36 No.1
In this paper, we deal with the uniqueness problem for the power of p-adic meromorphic functions. The results obtained in this paper are the p-adic analogues and supplements of the theorems given by Yang and Zhang [Non-existence of meromorphic solution of a Fermat type functional equation, Aequationes Math. 76(2008), 140-150], Chen, Chen and Li [Uniqueness of difference operators of meromorphic functions, J. Ineq. Appl. 2012(2012), Art 48], Zhang [Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl. 367(2010), 401-408].
VALUE SHARING AND UNIQUENESS FOR THE POWER OF P-ADIC MEROMORPHIC FUNCTIONS
MENG, CHAO,LIU, GANG,ZHAO, LIANG The Korean Society for Computational and Applied M 2018 Journal of applied mathematics & informatics Vol.36 No.1
In this paper, we deal with the uniqueness problem for the power of p-adic meromorphic functions. The results obtained in this paper are the p-adic analogues and supplements of the theorems given by Yang and Zhang [Non-existence of meromorphic solution of a Fermat type functional equation, Aequationes Math. 76(2008), 140-150], Chen, Chen and Li [Uniqueness of difference operators of meromorphic functions, J. Ineq. Appl. 2012(2012), Art 48], Zhang [Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl. 367(2010), 401-408].
A linear operator and associated families of meromorphically multivalent functions of order a
M. K. Aouf,H. M. Srivastava 장전수학회 2006 Advanced Studies in Contemporary Mathematics Vol.13 No.1
Making use of a linear operator, which is defined here by means of the Hadamard product (or convolution), we introduce two novel subclasses $Q_{a,c}(p,\alpha ;A,B)$ and $Q_{a,c}^{+}(p,\alpha ;A,B)$ of meromorphically multivalent functions of order $\alpha$ $(0\leqq \alpha <p)$ in the punctured unit disk $\mathbb{U}^{\ast}$. The main object of the present paper is to investigate the various important properties and characteristics of these subclasses of meromorphically multivalent functions. We extend the familiar concept of neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions. We also derive many interesting results for the Hadamard products of functions belonging to the function class $Q_{a,c}^{+}(p,\alpha;A,B)$.
A new subclass of meromorphic functions associated with Bessel functions
Sujatha,B. Venkateswarlu,P. Thirupathi Reddy,S. Sridevi 한국전산응용수학회 2023 Journal of applied mathematics & informatics Vol.41 No.5
In this article, we are presenting and examining a subclass of Meromorphic univalent functions as stated by the Bessel function. We get disparities in terms of coefficients, properties of distortion, closure theorems, Hadamard product. Finally, for the class $ \Sigma^* (\wp,\ell,\hbar,\tau,c)$, we obtain integral transformations.
MEROMORPHIC FUNCTIONS PARTIALLY SHARED VALUES WITH THEIR SHIFTS
Lin, Weichuan,Lin, Xiuqing,Wu, Aidi Korean Mathematical Society 2018 대한수학회보 Vol.55 No.2
We prove some uniqueness theorems of nonconstant meromorphic functions partially sharing values with their shifts. As an application, we obtain a sufficient condition on periodic meromorphic functions. Moreover, some examples are given to illustrate that the conditions are sharp and necessary.
Sufficient conditions for univalence and study of a class of meromorphic univalent functions
Bappaditya Bhowmik,Firdoshi Parveen 대한수학회 2018 대한수학회보 Vol.55 No.3
In this article we consider the class $\mathcal{A}(p)$ which consists of functions that are meromorphic in the unit disc $\ID$ having a simple pole at $z=p\in (0,1)$ with the normalization $f(0)=0=f'(0)-1 $. First we prove some sufficient conditions for univalence of such functions in $\ID$. One of these conditions enable us to consider the class $\mathcal{V}_{p}(\lambda)$ that consists of functions satisfying certain differential inequality which forces univalence of such functions. Next we establish that $\mathcal{U}_{p}(\lambda)\subsetneq \mathcal{V}_{p}(\lambda)$, where $\mathcal{U}_{p}(\lambda)$ was introduced and studied in \cite{BF-1}. Finally, we discuss some coefficient problems for $\mathcal{V}_{p}(\lambda)$ and end the article with a coefficient conjecture.