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Volume 25, Issue 5
Normal Functions Concerning Shared Values

Xiaojing Wang

Commun. Math. Res., 25 (2009), pp. 472-478.

Published online: 2021-07

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  • Abstract

In this paper we discuss normal functions concerning shared values. We obtain the following result. Let $\mathcal{F}$ be a family of meromorphic functions in the unit disc ∆, and $a$ be a nonzero finite complex number. If for any $f ∈\mathcal{F}$, the zeros of $f$ are of multiplicity, $f$ and $f′$ share $a$, then there exists a positive number $M$ such that for any $f ∈ \mathcal{F}, (1 − |z|^2 ) \frac{|f′(z)|}{1 + |f(z)|^2}  ≤ M$.

  • Keywords

shared value, normal family, normal function.

  • AMS Subject Headings

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COPYRIGHT: © Global Science Press

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@Article{CMR-25-472, author = {Wang , Xiaojing}, title = {Normal Functions Concerning Shared Values}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {25}, number = {5}, pages = {472--478}, abstract = {

In this paper we discuss normal functions concerning shared values. We obtain the following result. Let $\mathcal{F}$ be a family of meromorphic functions in the unit disc ∆, and $a$ be a nonzero finite complex number. If for any $f ∈\mathcal{F}$, the zeros of $f$ are of multiplicity, $f$ and $f′$ share $a$, then there exists a positive number $M$ such that for any $f ∈ \mathcal{F}, (1 − |z|^2 ) \frac{|f′(z)|}{1 + |f(z)|^2}  ≤ M$.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19363.html} }
TY - JOUR T1 - Normal Functions Concerning Shared Values AU - Wang , Xiaojing JO - Communications in Mathematical Research VL - 5 SP - 472 EP - 478 PY - 2021 DA - 2021/07 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19363.html KW - shared value, normal family, normal function. AB -

In this paper we discuss normal functions concerning shared values. We obtain the following result. Let $\mathcal{F}$ be a family of meromorphic functions in the unit disc ∆, and $a$ be a nonzero finite complex number. If for any $f ∈\mathcal{F}$, the zeros of $f$ are of multiplicity, $f$ and $f′$ share $a$, then there exists a positive number $M$ such that for any $f ∈ \mathcal{F}, (1 − |z|^2 ) \frac{|f′(z)|}{1 + |f(z)|^2}  ≤ M$.

Wang , Xiaojing. (2021). Normal Functions Concerning Shared Values. Communications in Mathematical Research . 25 (5). 472-478. doi:
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