Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4614595 | Journal of Mathematical Analysis and Applications | 2016 | 11 Pages |
Abstract
For functions p(z)=1+∑n=1∞pnzn holomorphic in the unit disk, satisfying Rep(z)>0, we generalize two inequalities proved by Livingston [10] and [11] and simplify their proofs. One of our results states that |pn−wpkpn−k|≤2max{1,|1−2w|}|pn−wpkpn−k|≤2max{1,|1−2w|}, w∈Cw∈C. Another result involves certain determinants whose entries are the coefficients pnpn. Both results are sharp. As applications we provide a simple proof of a theorem of Brown [2] and various inequalities for the coefficients of holomorphic self-maps of the unit disk.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Iason Efraimidis,