A note on a famous theorem of Pang and Zalcman
Feng L\"u, Junfeng Xu, Hongxun Yi
TL;DR
This paper improves a well-known theorem by Pang and Zalcman related to normal families in complex analysis, providing new results, necessary conditions, and illustrative examples.
Contribution
It offers an enhanced version of Pang and Zalcman's theorem, establishing stronger conditions and demonstrating their necessity with examples.
Findings
Established an improved theorem on normal families
Provided examples showing necessity of conditions
Strengthened understanding of Pang and Zalcman's original result
Abstract
In this paper, by studying the famous theorem of Pang and Zalcman, we find a normal family and obtain a result, which is an improvement of Pang and Zalcman's theorem in some sense. Meanwhile, several examples are provided to show that our result's conditions are necessary.
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Taxonomy
TopicsMeromorphic and Entire Functions · Fixed Point Theorems Analysis · Holomorphic and Operator Theory