Results 11 to 20 of about 66 (66)
Multivalent functions and QK spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 48, Page 2537-2546, 2004., 2004 We give a criterion for q‐valent analytic functions in the unit disk to belong to QK, a Möbius‐invariant space of functions analytic in the unit disk in the plane for a nondecreasing function K : [0, ∞) → [0, ∞), and we show by an example that our condition is sharp.
Hasi Wulan
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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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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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Further study on the Brück conjecture and some non-linear complex differential equations [PDF]
Arab Journal of Mathematical Sciences, 2021 Purpose – The purpose of this current paper is to deal with the study of non-constant entire solutions of some non-linear complex differential equations in connection to Brück conjecture, by using the theory of complex differential equation.
Dilip Chandra Pramanik, Kapil Roy
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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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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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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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Uniqueness of meromorphic functions sharing two finite sets
Open Mathematics, 2017 We prove uniqueness theorems of meromorphic functions, which show how two meromorphic functions are uniquely determined by their two finite shared sets. This answers a question posed by Gross.
Chen Jun-Fan
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Entire solutions for several complex partial differential-difference equations of Fermat type in ℂ2
Open Mathematics, 2021 By utilizing the Nevanlinna theory of meromorphic functions in several complex variables, we mainly investigate the existence and the forms of entire solutions for the partial differential-difference equation of Fermat type α∂f(z1,z2)∂z1+β∂f(z1,z2)∂z2m+f(
Gui Xian Min +3 more
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