N. Tuneski

activity

20182025

most citedHankel determinant for a class of analytic functions

12 citations · 28 across the 31 of their papers we have counts for

collaborators

37 papers

math.CV2025

On certain applications of grunsky coefficients in the theory of univalent functions

M. Obradovic, N. Tuneski

In this paper a survey is given of application of a method based on Grunsky coefficients for obtaining different estimates (some sharp) for the general class of univalent functions…

math.CV2025

Symmetric Toeplitz determinants of some classes of univalent functions

Milutin Obradović, Nikola Tuneski

In this paper, we consider estimates of symmetric Toeplitz determinants $T_{q, n} (f)$ for the class $U$ and for the general class $S$ for certain values of $q$ …

math.CV2025

On the difference of the two initial logarithmic coefficients for Bazilevic class of univalent functions

M. Obradovic, N. Tuneski

In this paper we give sharp bounds of the difference of the moduli of the second and the first logarithmic coefficient for Bazilevič class of univalent functions.

math.CV2024

Simple proofs of certain results on generalized Fekete-Szegő functional in the class $S$

Teodor Bulboacă, Milutin Obradović, Nikola Tuneski

In this paper we give simple proofs for the main results concerning generalized Fekete-Szegő functional of type $a_{3} (f) - λ a_{2} (f)^{2} - μ ∣ a_{2} (f) ∣$ , where $λ\in\mathb…

math.CV2024

Improvements of certain results of the class $S$ of univalent functions

Milutin Obradović, Nikola Tuneski

For $f \in S$ , the class univalent functions in the unit disk $D$ and given by $f (z) = z + \sum_{n = 2}^{\infty} a_{n} z^{n}$ for $z \in D$ , we improve previous bou…

math.CV2024

An improvement of the estimates of the modulus of the Hankel determinants of second and third order for the class $S$ of univalent functions

Milutin Obradović, Nikola Tuneski

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 $S$ o…

math.CV2024

New criteria for starlikeness in the unit disc

Milutin Obradović, Nikola Tuneski

It is well-known that the condition $Re [1 + \frac{z f ^{''} ( z )}{f ^{'} ( z )}] > 0$ , $z \in D$ , implies that $f$ is starlike function (i.e. convexity implies s…

math.CV2024

On the difference of the moduli of the two initial logarithmic coefficients

Milutin Obradović, Nikola Tuneski

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 $U$ , for the $α$ -con…

math.CV2023

Simple proofs of certain inequalities with logarithmic coefficients of univalent functions

Milutin Obradovic, Nikola Tuneski

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…

math.CV2023

On the difference of initial logarithmic coefficients for the class of univalent functions

Milutin Obradovic, Nikola Tuneski

In this paper we give estimates of the differences $∣ γ_{3} ∣ - ∣ γ_{2} ∣$ and $∣ γ_{4} ∣ - ∣ γ_{3} ∣$ for the class of functions $f$ univalent in the unit disc and normalized by $f (0) = f^{'} (0) - 1 = 0$ . Her…

math.CV2023

On a special class of Schwartz functions

Milutin Obradovic, Nikola Tuneski

In this paper we study functions $ω (z) = c_{1} z + c_{2} z^{2} + c_{3} z^{3} + \dots$ analytic in the open unit disk $D$ and such that $∣ ω^{'} (z) ∣ \leq 1$ for all $z \in D$ . For these f…

math.CV2023

Sharp bounds of logarithmic coefficients for a class of univalent functions

Milutin Obradović, Nikola Tuneski

Let $U (α, λ)$ , $0 < α < 1$ , $0 < λ < 1$ be the class of functions $f (z) = z + a_{2} z^{2} + a_{3} z^{3} + \dots$ satisfying $(\frac{z}{f ( z )})^{1 + α} f^{'} (z) - 1 < λ$ i…

math.CV2022

Two types of the second Hankel determinant for the class $U$ and the general class $S$

Milutin Obradović, Nikola Tuneski

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 $\math…

math.CV2022★ 1 cited

Hankel determinant of type $H_{2} (3)$ for inverse functions of some classes of univalent functions with missing second coefficient

Milutin Obradović, Nikola Tuneski

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 $H_{2} (3) (f) = a_{3} a_{5} - a_{4}^{2}$ …

math.CV2022

Two applications of Grunsky coefficients in the theory of univalent functions

Milutin Obradović, Nikola Tuneski

Let $S$ denote the class of functions $f$ which are analytic and univalent in the unit disk $D = {z : ∣ z ∣ < 1}$ and normalized with $f(z)=z+\sum_{n=2}^{\infty} a_n…

math.CV2021

Certain properties of the class of univalent functions with real coefficients

Milutin Obradović, Nikola Tuneski

Let $U^{+}$ be the class of analytic functions $f$ such that $\frac{z}{f ( z )}$ has real and positive coefficients and $f^{- 1}$ be its inverse. In this paper we give sharp e…

math.CV2021

The Fekete--Szegö problem and filtration of generators

Mark Elin, Fiana Jacobzon, Nikola Tuneski

In this paper we study an interpolation problem involving the Fekete--Szegö functional. It turns out that this problem links to the so-called filtration of infinitesimal generators…

math.CV2021

Coefficients of the inverse of functions for the subclass of $U (λ)$

Milutin Obradović, Nikola Tuneski

Let $A$ be the class of functions $f$ that are analytic in the unit disk $D$ and normalized such that $f (z) = z + a_{2} z^{2} + a_{3} z^{3} + \dots$ . Let $0 < λ \leq 1$ and \[ {\mat…

math.CV2021

Sharp bounds of Hankel determinants of second and third order for inverse functions of certain class of univalent functions

Milutin Obradović, Nikola Tuneski

Let $A$ be the class of functions that are analytic in the unit disc $D$ , normalized such that $f (z) = z + \sum_{n = 2}^{\infty} a_{n} z^{n}$ , and let class ${\mathcal U}(λ…

math.CV2020

On certain properties of some subclasses of univalent functions

Nikola Tuneski, Milutin Obradović

In this paper we determine the disks $∣ z ∣ < r \leq 1$ where for different classes of univalent functions, we have the property $${\rm Re}\left\{2\frac{zf'(z)}{f(z)}-\frac{z f''(z)}{f'(z…

math.CV2020

On a conjecture for the fifth coefficients for the class $U (λ)$

Milutin Obradović, Nikola Tuneski

Let $f$ be function that is analytic in the unit disk $D = {z : ∣ z ∣ < 1}$ , normalized such that $f (0) = f^{'} (0) - 1 = 0$ , i.e., of type $f (z) = z + \sum_{n = 2}^{\infty} a_{n} z^{n}$ . If addit…

math.CV2020

Some application of Grunsky coefficients in the theory of univalent functions

Milutin Obradović, Nikola Tuneski

Let function $f$ be normalized, analytic and univalent in the unit disk $D = {z : ∣ z ∣ < 1}$ and $f (z) = z + \sum_{n = 2}^{\infty} a_{n} z^{n}$ . Using a method based on Grusky coefficie…

math.CV2020

On certain properties of the class $U (λ)$

N. M. Alarifi, M. Obradovic, N. Tuneski

Let $A$ be the class of functions analytic in the unit disk $D := {z \in C : ∣ z ∣ < 1}$ and normalized such that $f (z) = z + a_{2} z^{2} + a_{3} z^{3} + \dots$ . In…

math.CV2020★ 1 cited

Zalcman and generalized Zalcman conjecture for the class $U$

Milutin Obradović, Nikola Tuneski

Function $f (z) = z + \sum_{n = 2}^{\infty} a_{n} z^{n}$ , normalized, analytic and univalent in the unit disk $D = {z : ∣ z ∣ < 1}$ , belongs to the class $U$ . if, and only if, \[…

On certain applications of grunsky coefficients in the theory of univalent functions

Symmetric Toeplitz determinants of some classes of univalent functions

On the difference of the two initial logarithmic coefficients for Bazilevic class of univalent functions

Simple proofs of certain results on generalized Fekete-Szegő functional in the class S

Improvements of certain results of the class S of univalent functions

An improvement of the estimates of the modulus of the Hankel determinants of second and third order for the class S of univalent functions

New criteria for starlikeness in the unit disc

On the difference of the moduli of the two initial logarithmic coefficients

Simple proofs of certain inequalities with logarithmic coefficients of univalent functions

On the difference of initial logarithmic coefficients for the class of univalent functions

On a special class of Schwartz functions

Sharp bounds of logarithmic coefficients for a class of univalent functions

Two types of the second Hankel determinant for the class U and the general class S

Hankel determinant of type H2​(3) for inverse functions of some classes of univalent functions with missing second coefficient

Two applications of Grunsky coefficients in the theory of univalent functions

Certain properties of the class of univalent functions with real coefficients

The Fekete--Szegö problem and filtration of generators

Coefficients of the inverse of functions for the subclass of U(λ)

Sharp bounds of Hankel determinants of second and third order for inverse functions of certain class of univalent functions

On certain properties of some subclasses of univalent functions

On a conjecture for the fifth coefficients for the class U(λ)

Some application of Grunsky coefficients in the theory of univalent functions

On certain properties of the class U(λ)

Zalcman and generalized Zalcman conjecture for the class U

Simple proofs of certain results on generalized Fekete-Szegő functional in the class $S$

Improvements of certain results of the class $S$ of univalent functions

An improvement of the estimates of the modulus of the Hankel determinants of second and third order for the class $S$ of univalent functions

Two types of the second Hankel determinant for the class $U$ and the general class $S$

Hankel determinant of type $H_{2} (3)$ for inverse functions of some classes of univalent functions with missing second coefficient

Coefficients of the inverse of functions for the subclass of $U (λ)$

On a conjecture for the fifth coefficients for the class $U (λ)$

On certain properties of the class $U (λ)$

Zalcman and generalized Zalcman conjecture for the class $U$