• 제목/요약/키워드: meromorphic functions

검색결과 191건 처리시간 0.022초

SUFFICIENT CONDITIONS FOR UNIVALENCE AND STUDY OF A CLASS OF MEROMORPHIC UNIVALENT FUNCTIONS

  • Bhowmik, Bappaditya;Parveen, Firdoshi
    • 대한수학회보
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    • 제55권3호
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    • pp.999-1006
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    • 2018
  • In this article we consider the class ${\mathcal{A}}(p)$ which consists of functions that are meromorphic in the unit disc $\mathbb{D}$ having a simple pole at $z=p{\in}(0,1)$ with the normalization $f(0)=0=f^{\prime}(0)-1$. First we prove some sufficient conditions for univalence of such functions in $\mathbb{D}$. One of these conditions enable us to consider the class ${\mathcal{A}}_p({\lambda})$ that consists of functions satisfying certain differential inequality which forces univalence of such functions. Next we establish that ${\mathcal{U}}_p({\lambda}){\subsetneq}{\mathcal{A}}_p({\lambda})$, where ${\mathcal{U}}_p({\lambda})$ was introduced and studied in [2]. Finally, we discuss some coefficient problems for ${\mathcal{A}}_p({\lambda})$ and end the article with a coefficient conjecture.

SETS AND VALUE SHARING OF q-DIFFERENCES OF MEROMORPHIC FUNCTIONS

  • Qi, Xiao-Guang;Yang, Lian-Zhong
    • 대한수학회보
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    • 제50권3호
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    • pp.731-745
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    • 2013
  • In this paper, we investigate uniqueness problems of certain types of $q$-difference polynomials, which improve some results in [20]. However, our proof is different from that in [20]. Moreover, we obtain a uniqueness result in the case where $q$-differences of two entire functions share values as well. This research also shows that there exist two sets, such that for a zero-order non-constant meromorphic function $f$ and a non-zero complex constant $q$, $E(S_j,f)=E(S_j,{\Delta}_qf)$ for $j=1,2$ imply $f(z)=t{\Delta}_qf$, where $t^n=1$. This gives a partial answer to a question of Gross concerning a zero order meromorphic function $f(z)$ and $t{\Delta}_qf$.

UNIQUENESS RESULTS ON MEROMORPHIC FUNCTIONS AND THEIR DIFFERENCE OPERATORS SHARING TARGETS WITH WEIGHT

  • Thu Thuy Hoang;Hong Nhat Nguyen;Duc Thoan Pham
    • 대한수학회보
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    • 제60권2호
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    • pp.461-473
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    • 2023
  • Let f be a nonconstant meromorphic function of hyper-order strictly less than 1, and let c ∈ ℂ \ {0} such that f(z + c) ≢ f(z). We prove that if f and its exact difference ∆cf(z) = f(z + c) - f(z) share partially 0, ∞ CM and share 1 IM, then ∆cf = f, where all 1-points with multiplicities more than 2 do not need to be counted. Some similar uniqueness results for such meromorphic functions partially sharing targets with weight and their shifts are also given. Our results generalize and improve the recent important results.

NEW SUBCLASS OF MEROMORPHIC MULTIVALENT FUNCTIONS ASSOCIATED WITH HYPERGEOMETRIC FUNCTION

  • Khadr, Mohamed A.;Ali, Ahmed M.;Ghanim, F.
    • Nonlinear Functional Analysis and Applications
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    • 제26권3호
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    • pp.553-563
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    • 2021
  • As hypergeometric meromorphic multivalent functions of the form $$L^{t,{\rho}}_{{\varpi},{\sigma}}f(\zeta)=\frac{1}{{\zeta}^{\rho}}+{\sum\limits_{{\kappa}=0}^{\infty}}{\frac{(\varpi)_{{\kappa}+2}}{{(\sigma)_{{\kappa}+2}}}}\;{\cdot}\;{\frac{({\rho}-({\kappa}+2{\rho})t)}{{\rho}}}{\alpha}_{\kappa}+_{\rho}{\zeta}^{{\kappa}+{\rho}}$$ contains a new subclass in the punctured unit disk ${\sum_{{\varpi},{\sigma}}^{S,D}}(t,{\kappa},{\rho})$ for -1 ≤ D < S ≤ 1, this paper aims to determine sufficient conditions, distortion properties and radii of starlikeness and convexity for functions in the subclass $L^{t,{\rho}}_{{\varpi},{\sigma}}f(\zeta)$.

MEROMORPHIC SOLUTIONS OF SOME NON-LINEAR DIFFERENCE EQUATIONS WITH THREE EXPONENTIAL TERMS

  • Min-Feng Chen;Zong-Sheng Gao;Xiao-Min Huang
    • 대한수학회보
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    • 제61권3호
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    • pp.745-762
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    • 2024
  • In this paper, we study the existence of finite order meromorphic solutions of the following non-linear difference equation fn(z) + Pd(z, f) = p1eα1z + p2eα2z + p3eα3z, where n ≥ 2 is an integer, Pd(z, f) is a difference polynomial in f of degree d ≤ n - 2 with small functions of f as its coefficients, pj (j = 1, 2, 3) are small meromorphic functions of f and αj (j = 1, 2, 3) are three distinct non-zero constants. We give the expressions of finite order meromorphic solutions of the above equation under some restrictions on αj (j = 1, 2, 3). Some examples are given to illustrate the accuracy of the conditions.

UNICITY OF MERMORPHIC FUNCTIONS CONCERNING SHARED FUNCTIONS WITH THEIR DIFFERENCE

  • Deng, Bingmao;Fang, Mingliang;Liu, Dan
    • 대한수학회보
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    • 제56권6호
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    • pp.1511-1524
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    • 2019
  • In this paper, we investigate the uniqueness of meromorphic functions of finite order concerning sharing small functions and prove that if f(z) and ${\Delta}_cf(z)$ share a(z), b(z), ${\infty}$ CM, where a(z), b(z)(${\neq}{\infty}$) are two distinct small functions of f(z), then $f(z){\equiv}{\Delta}_cf(z)$. The result improves the results due to Li et al. ([9]), Cui et al. ([1]) and $L{\ddot{u}}$ et al. ([12]).

Value Distribution of L-functions and a Question of Chung-Chun Yang

  • Li, Xiao-Min;Yuan, Qian-Qian;Yi, Hong-Xun
    • Kyungpook Mathematical Journal
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    • 제61권3호
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    • pp.495-512
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    • 2021
  • We study the value distribution theory of L-functions and completely resolve a question from Yang [10]. This question is related to L-functions sharing three finite values with meromorphic functions. The main result in this paper extends corresponding results from Li [10].

SOME GROWTH ASPECTS OF SPECIAL TYPE OF DIFFERENTIAL POLYNOMIAL GENERATED BY ENTIRE AND MEROMORPHIC FUNCTIONS ON THE BASIS OF THEIR RELATIVE (p, q)-TH ORDERS

  • Biswas, Tanmay
    • Korean Journal of Mathematics
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    • 제27권4호
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    • pp.899-927
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    • 2019
  • In this paper we establish some results depending on the comparative growth properties of composite entire and meromorphic functions using relative (p, q)-th order and relative (p, q)-th lower order where p, q are any two positive integers and that of a special type of differential polynomial generated by one of the factors.

WEIGHTED SHARING AND UNIQUENESS OF ENTIRE OR MEROMORPHIC FUNCTIONS

  • Bhoosnurmath, Subhas S.;Pujari, Veena L.
    • 대한수학회보
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    • 제52권1호
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    • pp.13-33
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    • 2015
  • In this paper, we study the uniqueness problems of entire or meromorphic functions concerning differential polynomials that share one value with multiplicity using weighted sharing method. We prove two main theorems which generalize and improve the results of Fang and Fang [2], Dyavanal [1] and others and also solve the open problem posed by Dyavanal. This method yields some new results.