Results 51 to 60 of about 113 (110)

On Transcendental Entire Solution of Fermat-Type Trinomial and Binomial Equations Under Restricted Hyper-Order

Annales Mathematicae Silesianae
In this paper we are focusing on finding the transcendental entire solution of Fermat-type trinomial and binomial equations, by restricting the hyper-order to be less than one.
Banerjee Abhijit, Sarkar Jhuma
doaj   +1 more source

Uniqueness of meromorphic functions concerning small functions and derivatives-differences

Demonstratio Mathematica
In this article, we study the unicity of meromorphic functions concerning small functions and derivatives-differences. The results obtained in this article extend and improve some results of Chen et al.
He Zhiying, Fang Mingliang, Xiao Jianbin
doaj   +1 more source

© Hindawi Publishing Corp. ORDER OF GROWTH OF SOLUTIONS TO ALGEBRAIC DIFFERENTIAL EQUATIONS IN THE UNIT DISK [PDF]

, 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.
L. R. Sons, D. Benbourenane
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A new result for entire functions and their shifts with two shared values

Open Mathematics
Let ff be a transcendental entire function of hyperorder strictly less than 1, and let cc be a nonzero finite complex number. We prove that if f(z)f\left(z) and f(z+c)f\left(z+c) partially share 0, 1 ignoring multiplicity (i.e., E¯(0,f(z))⊆E¯(0,f(z+c ...
Xu Aizhu, Lin Peiqiang, Chen Shengjiang
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On Littlewood's Constants [PDF]

, 2017
In two papers, Littlewood studied seemingly unrelated constants: (i) the best α such that for any polynomial f, of degree n, the areal integral of its spherical derivative is at most ·nα, and (ii) the extremal growth rate rβ of the length of Green's ...
Beliaev, D., Smirnov, S.
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Characterizations of transcendental entire solutions of trinomial partial differential-difference equations in ℂ2#

Demonstratio Mathematica
This study is devoted to exploring the existence and the precise form of finite-order transcendental entire solutions of second-order trinomial partial differential-difference equations L(f)2+2hL(f)f(z1+c1,z2+c2)+f(z1+c1,z2+c2)2=eg(z1,z2)L{(f)}^{2}+2hL(f)
Xu Hong Yan, Haldar Goutam
doaj   +1 more source

Results on the deficiencies of some differential-difference polynomials of meromorphic functions

Open Mathematics, 2016
In this paper, we study the relation between the deficiencies concerning a meromorphic function f(z), its derivative f′(z) and differential-difference monomials f(z)mf(z+c)f′(z), f(z+c)nf′(z), f(z)mf(z+c).
Zheng Xiu-Min, Xu Hong-Yan
doaj   +1 more source

The existence of solutions to certain type of nonlinear difference-differential equations

Open Mathematics, 2018
In this paper we study the entire solutions to a certain type of difference-differential equations. We also give an affirmative answer to the conjecture of Zhang et al.
Lü Weiran, Wu Linlin, Wang Dandan, Yang Chungchun   +3 more
doaj   +1 more source

Nonlinear differential polynomial sharing a nonzero polynomial with certain degree: Dedicated to Professor Ioan A. Rus on the occasion of his 80th anniversary [PDF]

, 2016
In this paper we study the uniqueness problems of meromorphic functions when certain non-linear dierential polynomial sharing a nonzero polynomial with certain degree.
MAJUMDER, Sujoy, BANERJEE, Abhijit
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Linear differential polynomials in zero-free meromorphic functions [PDF]

The paper determines all meromorphic functions f in C such that f and F have finitely many zeros, where F = f (k) + ak−1f(k−1)+ ... + a0f with k ≥ 3 and the aj rational functions.
Langley, J.K.
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