Uniqueness of entire functions sharing an entire function of smaller order with their derivatives
type: Item
instance of: scholarly article
title: Uniqueness of entire functions sharing an entire function of smaller order with their derivatives
zbMATH Open document ID: 1243.30069
author: Xiao-Min Li
author: Hongxun Yi
published in: Journal of Mathematical Sciences (New York)
publication date: 2011-07-12T00:00:00Z
review text: In 1996, \textit{R. Brück} [Result. Math. 30, No. 1--2, 21--24 (1996; Zbl 0861.30032)] conjectured that if \(f\) is a non-constant entire function satisfying \(\sigma_{2}(f) < \infty\), where the hyper-order \(\sigma_{2}(f)\) of \(f\) is not a positive integer, and if \(f\) and \(f'\) share one finite complex number \(a\) CM, then \(f - a = c(f' - a)\) for some constant \(c\neq 0\). This conjecture inspired a lot of researchers to work on the uniqueness problem of an entire function and its derivatives. The present paper also deals with such problems. A number of interesting results are proved in the paper, which involve the sharing of an entire function having slower growth than that of the function sharing it with derivatives.
reviewed by: Indrajit Lahiri
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 5919508
zbMATH Keywords: entire function
zbMATH Keywords: uniqueness
zbMATH Keywords: derivative
zbMATH Keywords: order
MaRDI profile type: Publication
full work available at URL: s10958-011-0329-3
OpenAlex ID: W2036580022
cites work: On meromorphic functions that share one value with their derivative
cites work: On entire functions which share one value CM with their first derivative
cites work: Q3605803
cites work: Entire functions that share a small function with their derivatives
cites work: On conjecture of R.Brück concerning the entire function sharing one value CM with its derivative
cites work: Some further results on the zeros and growths of entire solutions to second order linear differential equations
cites work: Q5810707
cites work: Entire functions that share one value with one or two of their derivatives
cites work: Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity
cites work: Q3995409
cites work: Nevanlinna theory and complex differential equations
cites work: Q4821517
cites work: On a kth-order differential equation
cites work: Entire functions sharing one polynomial with their derivatives
cites work: An entire function and its derivatives sharing a polynomial
cites work: On uniqueness of an entire function and its derivatives
cites work: Some results on the regular solutions of a linear differential equation
cites work: Some further results on entire functions sharing a polynomial with their linear differential polynomials
cites work: On the uniqueness of an entire function sharing a small entire function with some linear differential polynomial
cites work: Uniqueness of meromorphic functions sharing a meromorphic function of a smaller order with their derivatives
cites work: Entire functions that share a polynomial with one of their derivatives
cites work: Uniqueness of entire functions and their derivatives
cites work: The uniqueness of an entire function sharing a small entire function with its derivatives
cites work: Q5505295
cites work: Q4274978
cites work: Q4827955
cites work: Q5717263
cites work: Q5433865
cites work: Q3432916
DOI: 10.1007/S10958-011-0329-3
description: scientific article; zbMATH DE number 5919508