5 citations · 13 across the 18 of their papers we have counts for
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Differential inequalities and a Marty-type criterion for quasi-normality
Jürgen Grahl, Tomer Manket, Shahar Nevo
We show that the family of all holomorphic functions in a domain satisfying $$\frac{|f^{(k)}|}{1+|f|}(z)\le C \qquad \mbox{ for all } z\in D$$ (where is a natural numbe…
Quasi-normality induced by differential inequalities
Jürgen Grahl, Shahar Nevo
We show that the family of all meromorphic functions in a domain satisfying $$\frac{|f^{(k)}|}{1+|f|}(z)\ge C \qquad \mbox{ for all } z\in D$$ (where is a…
Differential inequalities and quasi-normal families
Roi Bar, Jürgen Grahl, Shahar Nevo
We show that a family of meromorphic functions in a domain satisfying $$\frac{|f^{(k)}|}{1+|f^{(j)}|^α}(z)\ge C \qquad \mbox{for all} z\in D \mbox{and all} f\in {\ca…
An extension of one direction in Marty's normality criterion
J. Grahl, S. Nevo
We prove an extension of one direction in Marty's theorem where the spherical derivative is replaced by a more general quantity involving higher derivatives.
Differential inequality of the second derivative that leads to normality
Qiaoyu Chen, Shahar Nevo, XueCheng Pang
Let F be a family of functions meromorphic in a domain D. If {|f|/(1+|f|^3):f in F} is locally uniformly bounded away from zero, then F is normal.
A criterion of normality based on a single holomorphic function II
Xiaojun Liu, Shahar Nevo
In this paper, we continue to discuss normality based on a single\linebreak holomorphic function. We obtain the following result. Let $\CF$ be a family of functions holomorphic on…