Zobrazeno 1 - 10
of 144
pro vyhledávání: '"Obradović, Milutin"'
Autor:
Obradović, Milutin, Tuneski, Nikola
For $f\in \mathcal{S}$, the class univalent functions in the unit disk $\mathbb{D}$ and given by $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$ for $z\in \mathbb{D}$, we improve previous bounds for the second and third Hankel determinants in case when either $
Externí odkaz:
http://arxiv.org/abs/2411.13102
Autor:
Obradović, Milutin, Tuneski, Nikola
Using some properties of the Grunsky coefficients we improve earlier results for upper bounds of the Hankel determinants of the second and third order for the class $\mathcal{S}$ of univalent functions.
Externí odkaz:
http://arxiv.org/abs/2411.12378
Autor:
Obradović, Milutin, Tuneski, Nikola
It is well-known that the condition ${\operatorname{Re}} \left[1+\frac{zf''(z)}{f'(z)}\right]>0$, $z\in{\mathbb D}$, implies that $f$ is starlike function (i.e. convexity implies starlikeness). If the previous condition is not satisfied for every $z\
Externí odkaz:
http://arxiv.org/abs/2405.07997
Autor:
Obradović, Milutin, Tuneski, Nikola
In this paper, we give sharp bounds of the difference of the moduli of the second and the first logarithmic coefficient for the functions on the class $\mathcal U$, for the $\alpha$-convex functions, and for the class $\mathcal{G}(\alpha)$ introduced
Externí odkaz:
http://arxiv.org/abs/2404.01303
Autor:
Obradovic, Milutin, Tuneski, Nikola
In this paper we give simple proofs for the bounds (some of them sharp) of the difference of the moduli of the second and the first logarithmic coefficient for the general class of univalent functions and for the class of convex univalent functions.
Externí odkaz:
http://arxiv.org/abs/2311.09901
Autor:
Obradovic, Milutin, Tuneski, Nikola
In this paper we study functions $ \omega(z) = c_1z+c_2z^2+c_3z^3+\cdots$ analytic in the open unit disk ${\mathbb D}$ and such that $|\omega'(z)|\le1$ for all $z\in{\mathbb D}$. For these functions we give estimates (sometimes sharp) for the followi
Externí odkaz:
http://arxiv.org/abs/2311.06277
Autor:
Obradović, Milutin, Tuneski, Nikola
Let $\mathcal{U(\alpha, \lambda)}$, $0<\alpha <1$, $0 < \lambda <1$ be the class of functions $f(z)=z+a_{2}z^{2}+a_{3}z^{3}+\cdots$ satisfying $$\left|\left(\frac{z}{f(z)}\right)^{1+\alpha}f'(z)-1\right|<\lambda$$ in the unit disc ${\mathbb D}$. For
Externí odkaz:
http://arxiv.org/abs/2304.12920
Autor:
Obradović, Milutin, Tuneski, Nikola
In this paper we determine the upper bounds of the Hankel determinants of special type $H_{2}(3)(f)$ and $H_{2}(4)(f)$ for the class of univalent functions and for the class $\mathcal{U}$ defined by \[ \mathcal{U}=\left\{ f\in\mathcal{A} : \left|\lef
Externí odkaz:
http://arxiv.org/abs/2212.06771
Autor:
Obradović, Milutin, Tuneski, Nikola
In this paper we determine the upper bounds of $|H_{2}(3)|$ for the inverse functions of functions of some classes of univalent functions, where $H_{2}(3)(f)=a_{3}a_{5}-a_{4}^{2}$ is the Hankel determinant of a special type.
Externí odkaz:
http://arxiv.org/abs/2211.12325
Autor:
Obradović, Milutin, Tuneski, Nikola
Let $\mathcal{S}$ denote the class of functions $f$ which are analytic and univalent in the unit disk ${\mathbb D}=\{z:|z|<1\}$ and normalized with $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$. Using a method based on Grusky coefficients we study two problem
Externí odkaz:
http://arxiv.org/abs/2201.07336