• Title/Summary/Keyword: Meromorphic

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A CRITERION FOR BOUNDED FUNCTIONS

  • Nunokawa, Mamoru;Owa, Shigeyoshi;Sokol, Janusz
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.1
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    • pp.215-225
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    • 2016
  • We consider a sufficient condition for w(z), analytic in ${\mid}z{\mid}$ < 1, to be bounded in ${\mid}z{\mid}$ < 1, where $w(0)=w^{\prime}(0)=0$. We apply it to the meromorphic starlike functions. Also, a certain Briot-Bouquet differential subordination is considered. Moreover, we prove that if $p(z)+zp^{\prime}(z){\phi}(p(z)){\prec}h(z)$, then $p(z){\prec}h(z)$, where $h(z)=[(1+z)(1-z)]^{\alpha}$, under some additional assumptions on ${\phi}(z)$.

FINITE LOGARITHMIC ORDER SOLUTIONS OF LINEAR q-DIFFERENCE EQUATIONS

  • Wen, Zhi-Tao
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.1
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    • pp.83-98
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    • 2014
  • During the last decade, several papers have focused on linear q-difference equations of the form ${\sum}^n_{j=0}a_j(z)f(q^jz)=a_{n+1}(z)$ with entire or meromorphic coefficients. A tool for studying these equations is a q-difference analogue of the lemma on the logarithmic derivative, valid for meromorphic functions of finite logarithmic order ${\rho}_{log}$. It is shown, under certain assumptions, that ${\rho}_{log}(f)$ = max${{\rho}_{log}(a_j)}$ + 1. Moreover, it is illustrated that a q-Casorati determinant plays a similar role in the theory of linear q-difference equations as a Wronskian determinant in the theory of linear differential equations. As a consequence of the main results, it follows that the q-gamma function and the q-exponential functions all have logarithmic order two.

EXISTENCE OF TRANSCENDENTAL MEROMORPHIC SOLUTIONS ON SOME TYPES OF NONLINEAR DIFFERENTIAL EQUATIONS

  • Hu, Peichu;Liu, Manli
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.4
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    • pp.991-1002
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    • 2020
  • We show that when n > m, the following delay differential equation fn(z)f'(z) + p(z)(f(z + c) - f(z))m = r(z)eq(z) of rational coefficients p, r doesn't admit any transcendental entire solutions f(z) of finite order. Furthermore, we study the conditions of α1, α2 that ensure existence of transcendental meromorphic solutions of the equation fn(z) + fn-2(z)f'(z) + Pd(z, f) = p1(z)eα1(z) + p2(z)eα2(z). These results have improved some known theorems obtained most recently by other authors.

GENERALIZATION CLASS OF CERTAIN MEROMORPHIC UNIVALENT FUNCTIONS WITH POSITIVE COEFFICIENTS

  • Cho, Nak Eun;Qwa, Shigeyoshi;Lee, Sang Hun;Altintas, Qsman
    • Kyungpook Mathematical Journal
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    • v.29 no.2
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    • pp.133-139
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    • 1989
  • A generalization class $\sum_{P}$(${\alpha}$, ${\beta}$, ${\gamma}$) of certain meromorphic univalent functions with positive coefficients is introduced. The class $\sum_{P}$(${\alpha}$, ${\beta}$, ${\gamma}$) is a generalization of the class which was stuied by N.E. Cho, S.H. Lee and S. Qwa [1]. The object of the present paper is to prove some properties of functions in the class $\sum_{P}$(${\alpha}$, ${\beta}$, ${\gamma}$).

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Zeros and Uniqueness of Difference Polynomials of Meromorphic Functions

  • Qi, Xiaoguang;Dou, Jia
    • Kyungpook Mathematical Journal
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    • v.53 no.4
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    • pp.541-552
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    • 2013
  • This research is a continuation of a recent paper due to the first author in [9]. Different from previous results, we investigate the value distribution of difference polynomials of moromorphic functions in this paper. In particular, we are interested in the existence of zeros of $f(z)^n({\lambda}f(z+c)^m+{\mu}f(z)^m)-a$, where f is a moromorphic function, n, m are two non-negative integers, and ${\lambda}$, ${\mu}$ are non-zero complex numbers. However, the proof here is obviously different to the one in [9]. We also study difference polynomials of entire functions sharing a common value, which improves the result in [10, 13].

Some properties of a Certain family of Meromorphically Univalent Functions defined by an Integral Operator

  • Aghalary, Rasoul
    • Kyungpook Mathematical Journal
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    • v.48 no.3
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    • pp.379-385
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    • 2008
  • Making use of a linear operator, we introduce certain subclass of meromorphically univalent functions in the punctured unit disk and study its properties including some inclusion results, coefficient and distortion problems. Our result generalize many results known in the literature.