Results 21 to 30 of about 115 (110)
Order of growth of solutions to algebraic differential equations in the unit disk
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 41, Page 2161-2170, 2004., 2004 S. B. Bank has shown that there is no uniform growth estimate for meromorphic solutions of algebraic differential equations with meromorphic coefficients in the unit disk. We give conditions under which such solutions must have a finite order of growth.
D. Benbourenane, L. R. Sons
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A class of gap series with small growth in the unit disc
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 1, Page 29-40, 2002., 2002 Let β > 0 and let α be an integer which is at least 2. If f is an analytic function in the unit disc D which has power series representation f(z)=∑k=0∞ak zkα, limsupk→∞ (log+|ak|/logk) = α(1 + β), then the first author has proved that f is unbounded in every sector {z ∈ D : Φ − ϵ < argz < Φ + ϵ, for ϵ > 0}.
L. R. Sons, Zhuan Ye
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Some results on a question of Li, Yi and Li [PDF]
, 2019 The purpose of this paper is to study the uniqueness problems of certain difference polynomials of meromorphic functions sharing a nonzero polynomial. The results of this paper improve and generalize some recent results due to Li, Yi and Li [11].
MAJUMDER , Sujoy, BANERJEE , Abhijit
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International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 7, Page 425-427, 2001., 2001 We prove that Mues′ conjecture holds for the second‐ and higher‐order derivatives of a square and higher power of any transcendental meromorphic function.
Indrajit Lahiri
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Meromorphic solutions of certain nonlinear difference equations
Open Mathematics, 2020 This paper focuses on finite-order meromorphic solutions of nonlinear difference equation fn(z)+q(z)eQ(z)Δcf(z)=p(z){f}^{n}(z)+q(z){e}^{Q(z)}{\text{Δ}}_{c}f(z)=p(z), where p,q,Qp,q,Q are polynomials, n≥2n\ge 2 is an integer, and Δcf{\text{Δ}
Liu Huifang, Mao Zhiqiang, Zheng Dan
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Value distribution of certain differential polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 2, Page 83-91, 2001., 2001 We prove a result on the value distribution of differential polynomials which improves some earlier results.
Indrajit Lahiri
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Unicity of meromorphic functions concerning differences and small functions
Open Mathematics, 2022 In this paper, we study the unicity of meromorphic functions concerning differences and small functions and mainly prove two results: 1. Let ff be a transcendental entire function of finite order with a Borel exceptional entire small function a(z)a\left ...
He Zhiying, Xiao Jianbin, Fang Mingliang
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A note on a result of Singh and Kulkarni
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 4, Page 285-288, 2000., 2000 We prove that if f is a transcendental meromorphic function of finite order and ∑a≠∞δ(a, f) + δ(∞, f) = 2, then K(f(k))=2k(1−δ(∞,f))1+k−kδ(∞,f) , where K(f(k))=limr→∞N(r,1/f(k))+N(r,f(k))T(r,f(k)) This result improves a result by Singh and Kulkarni.
Mingliang Fang
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Some unsolved problems on meromorphic functions of uniformly bounded characteristic
International Journal of Mathematics and Mathematical Sciences, Volume 8, Issue 3, Page 477-482, 1985., 1985 The family UBC(R) of meromorphic functions of uniformly bounded characteristic in a Rieman surface R is defined in terms of the Shimizu‐Ahlfors characteristic function. There are some natural parallels between UBC(R) and BMOA(R), the family of holomorphic functions of bounded mean oscillation in R.
Shinji Yamashita
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The uniqueness of meromorphic functions in k-punctured complex plane
Open Mathematics, 2017 The main purpose of this paper is to investigate the uniqueness of meromorphic functions that share two finite sets in the k-punctured complex plane. It is proved that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 5, such that any two admissible ...
Xu Hong Yan, Liu San Yang
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