Currently displaying 1 – 11 of 11

Showing per page

Order by Relevance | Title | Year of publication

Uniqueness of entire functions and fixed points

Xiao-Guang QiLian-Zhong Yang — 2010

Annales Polonici Mathematici

Let f and g be entire functions, n, k and m be positive integers, and λ, μ be complex numbers with |λ| + |μ| ≠ 0. We prove that ( f ( z ) ( λ f m ( z ) + μ ) ) ( k ) must have infinitely many fixed points if n ≥ k + 2; furthermore, if ( f ( z ) ( λ f m ( z ) + μ ) ) ( k ) and ( g ( z ) ( λ g m ( z ) + μ ) ) ( k ) have the same fixed points with the same multiplicities, then either f ≡ cg for a constant c, or f and g assume certain forms provided that n > 2k + m* + 4, where m* is an integer that depends only on λ.

The zero distribution and uniqueness of difference-differential polynomials

Kai LiuXin-Ling LiuLian-Zhong Yang — 2013

Annales Polonici Mathematici

We consider the zero distribution of difference-differential polynomials of meromorphic functions and present some results which can be seen as the discrete analogues of the Hayman conjecture. In addition, we also investigate the uniqueness of difference-differential polynomials of entire functions sharing one common value. Our theorems improve some results of Luo and Lin [J. Math. Anal. Appl. 377 (2011), 441-449] and Liu, Liu and Cao [Appl. Math. J. Chinese Univ. 27 (2012), 94-104].

Matrix inequalities involving the Khatri-Rao product

Xian ZhangZhong Peng YangChong-Guang Cao — 2002

Archivum Mathematicum

We extend three inequalities involving the Hadamard product in three ways. First, the results are extended to any partitioned blocks Hermitian matrices. Second, the Hadamard product is replaced by the Khatri-Rao product. Third, the necessary and sufficient conditions under which equalities occur are presented. Thereby, we generalize two inequalities involving the Khatri–Rao product.

Page 1

Download Results (CSV)