Dual Smale's mean value conjecture for $n=7$
We give an analytic proof of the dual Smale's mean value conjecture in the case $n=7$.
math.CV↗
arXiv subjects
Diana M. Khammatova
Publications and source records attributed to Diana M. Khammatova.
Weissler and Bernoulli type inequalities in Bergman spaces
We consider Weissler type inequalities for Bergman spaces with general radial weights and give conditions on the weight $w$ in terms of its moments ensuring that $\|f_r\|_{A^{2n}(w)}\leq \|f\|_{A^2(w)}$ whenever $n\in \mathbb{N}$ and $0< r\le 1/\sqrt{n}$. For noninteger exponents a special case of this inequality is proved which can be considered as a certain analog of the Bernoulli inequality. An example of a monotonic weight is constructed for which these inequalities are no longer true.
math.CV↗
The Bohr inequality for the generalized C{é}saro averaging operators
The main aim of this paper is to prove a generalization of the classical Bohr theorem and as an application, we obtain a counterpart of Bohr theorem for the generalized Cesáro operator.
math.CV↗
On a conjecture about univalent polynomials
In this paper we prove a recent conjecture formulated by Dmitrishin, Smorodin and Stokolos about that certain polynomials are univalent in the unit disk. As a consequence we get an upper estimate for the Koebe radius of univalent polynomials.
math.CV↗