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A generalization of Livingston's coefficient inequalities for functions with positive real part | | Iason Efraimidis
; | | Date: |
23 Jun 2015 | | Abstract: | For functions $p(z) = 1 + sum_{n=1}^infty p_n z^n$ holomorphic in the unit
disk, satisfying $ {
m Re}, p(z) > 0$, we generalize two inequalities proved
by Livingston in 1969 and 1985, and simplify their proofs. One of our results
is $|p_n -w p_k p_{n-k}|leq 2max{1, |1-2w|}, win{mathbb C}$, while the
other involves certain determinants whose entries are the coefficients $p_n$.
Both results are sharp. As an application we deduce two inequalities for
holomorphic self-maps of the unit disk. | | Source: | arXiv, 1506.7111 | | Services: | Forum | Review | PDF | Favorites | |
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