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Weak normal and quasinormal families of holomorphic curves

Si Duc Quang, Dau Hong Quan (2018)

Archivum Mathematicum

In this paper we introduce the notion of weak normal and quasinormal families of holomorphic curves from a domain in into projective spaces. We will prove some criteria for the weak normality and quasinormality of at most a certain order for such families of holomorphic curves.

Weakly Increasing Zero-Diminishing Sequences

Bakan, Andrew, Craven, Thomas, Csordas, George, Golub, Anatoly (1996)

Serdica Mathematical Journal

The following problem, suggested by Laguerre’s Theorem (1884), remains open: Characterize all real sequences {μk} k=0...∞ which have the zero-diminishing property; that is, if k=0...n, p(x) = ∑(ak x^k) is any P real polynomial, then k=0...n, p(x) = ∑(μk ak x^k) has no more real zeros than p(x). In this paper this problem is solved under the additional assumption of a weak growth condition on the sequence {μk} k=0...∞, namely lim n→∞ | μn |^(1/n) < ∞. More precisely, it is established that...

Weighted sharing and uniqueness of entire functions

Fengqin Wu, Yan Xu (2010)

Czechoslovak Mathematical Journal

In this paper we study the uniqueness for meromorphic functions sharing one value, and obtain some results which improve and generalize the related results due to M. L. Fang, X. Y. Zhang, W. C. Lin, T. D. Zhang, W. R. Lü and others.

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