• Title/Summary/Keyword: Entire function

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A NOTE ON VALUE DISTRIBUTION OF COMPOSITE ENTIRE FUNCTIONS

  • Lahiri, Indrajit
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.1-6
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    • 2001
  • We discuss the value distribution of composite entire functions including those of infinite order and estimate the number of Q-points of such functions for an entire function Q or relatively slower growth.

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RELATIVE LOGARITHMIC ORDER OF AN ENTIRE FUNCTION

  • Ghosh, Chinmay;Bandyopadhyay, Anirban;Mondal, Soumen
    • Korean Journal of Mathematics
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    • v.29 no.1
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    • pp.105-120
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    • 2021
  • In this paper, we extend some results related to the growth rates of entire functions by introducing the relative logarithmic order ����g(f) of a nonconstant entire function f with respect to another nonconstant entire function g. Next we investigate some theorems related the behavior of ����g(f). We also define the relative logarithmic proximate order of f with respect to g and give some theorems on it.

ON THE TRANSCENDENTAL ENTIRE SOLUTIONS OF A CLASS OF DIFFERENTIAL EQUATIONS

  • Lu, Weiran;Li, Qiuying;Yang, Chungchun
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.5
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    • pp.1281-1289
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    • 2014
  • In this paper, we consider the differential equation $$F^{\prime}-Q_1=Re^{\alpha}(F-Q_2)$$, where $Q_1$ and $Q_2$ are polynomials with $Q_1Q_2{\neq}0$, R is a rational function and ${\alpha}$ is an entire function. We consider solutions of the form $F=f^n$, where f is an entire function and $n{\geq}2$ is an integer, and we prove that if f is a transcendental entire function, then $\frac{Q_1}{Q_2}$ is a polynomial and $f^{\prime}=\frac{Q_1}{nQ_2}f$. This theorem improves some known results and answers an open question raised in [16].

UNIQUENESS RELATED TO HIGHER ORDER DIFFERENCE OPERATORS OF ENTIRE FUNCTIONS

  • Xinmei Liu;Junfan Chen
    • The Pure and Applied Mathematics
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    • v.30 no.1
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    • pp.43-65
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    • 2023
  • In this paper, by using the difference analogue of Nevanlinna's theory, the authors study the shared-value problem concerning two higher order difference operators of a transcendental entire function with finite order. The following conclusion is proved: Let f(z) be a finite order transcendental entire function such that λ(f - a(z)) < ρ(f), where a(z)(∈ S(f)) is an entire function and satisfies ρ(a(z)) < 1, and let 𝜂(∈ ℂ) be a constant such that ∆𝜂n+1 f(z) ≢ 0. If ∆𝜂n+1 f(z) and ∆𝜂n f(z) share ∆𝜂n a(z) CM, where ∆𝜂n a(z) ∈ S ∆𝜂n+1 f(z), then f(z) has a specific expression f(z) = a(z) + BeAz, where A and B are two non-zero constants and a(z) reduces to a constant.

Uniqueness of Entire Functions that Share an Entire Function of Smaller Order with One of Their Linear Differential Polynomials

  • Li, Xiao-Min;Yi, Hong-Xun
    • Kyungpook Mathematical Journal
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    • v.56 no.3
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    • pp.763-776
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    • 2016
  • We prove a uniqueness theorem of entire functions sharing an entire function of smaller order with their linear differential polynomials. The results in this paper improve the corresponding results given by Gundersen-Yang[4], Chang-Zhu[3], and others. Some examples are provided to show that the results in this paper are best possible.

SOME REMARKS ON THE GENERALIZED ORDER AND GENERALIZED TYPE OF ENTIRE MATRIX FUNCTIONS IN COMPLETE REINHARDT DOMAIN

  • Biswas, Tanmay;Biswas, Chinmay
    • Korean Journal of Mathematics
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    • v.29 no.4
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    • pp.811-824
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    • 2021
  • The main aim of this paper is to introduce the definitions of generalized order and generalized type of the entire function of complex matrices and then study some of their properties. By considering the concepts of generalized order and generalized type, we will extend some results of Kishka et al. [5].

RELATIVE (p, q) - 𝜑 ORDER BASED SOME GROWTH ANALYSIS OF COMPOSITE p-ADIC ENTIRE FUNCTIONS

  • Biswas, Tanmay;Biswas, Chinmay
    • Korean Journal of Mathematics
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    • v.29 no.2
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    • pp.361-370
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    • 2021
  • Let 𝕂 be a complete ultrametric algebraically closed field and 𝓐 (𝕂) be the 𝕂-algebra of entire function on 𝕂. For any p-adic entire functions f ∈ 𝓐 (𝕂) and r > 0, we denote by |f|(r) the number sup {|f (x)| : |x| = r} where |·|(r) is a multiplicative norm on 𝓐 (𝕂). In this paper we study some growth properties of composite p-adic entire functions on the basis of their relative (p, q)-𝜑 order where p, q are any two positive integers and 𝜑 (r) : [0, +∞) → (0, +∞) is a non-decreasing unbounded function of r.