arXiv subjects

Paweł Zaprawa

Publications and source records attributed to Paweł Zaprawa.

4 recordsLinked to original sources

arXiv2026

Higher-Order Schippers-Schwarzian Derivatives for Non-Circular Starlike Functions

We find sharp upper bounds for the initial higher-order Schippers-Schwarzian derivatives $σ_3(f)(0)$ and $σ_4(f)(0)$ for several subclasses of univalent and starlike functions in the unit disk. The functions in these classes are defined by subordination to domains bounded by an exponential-sine curve, a cardioid, or a petal-shaped curve. We determine the sharp bounds and find the corresponding extremal functions for each invariant in these subclasses. As an application, we also obtain sharp bounds for the initial Grunsky coefficients $ω_{1,1}$ and $ω_{1,2}$.

math.CV↗

arXiv2026

Sharp inequalities for Logarithmic Coefficients for Certain Classes of Univalent Functions

Let $\mathcal{S}$ denote the class of functions $f(z) = z + \sum_{n=2}^{\infty} a_n z^n$ that are analytic and univalent in the open unit disk $\mathbb{D} = \{z \in \mathbb{C} : |z| < 1\}$. In this paper, we determine the sharp bounds of the Toeplitz determinants whose entries are the logarithmic coefficients of $f \in \mathcal{S}$. Furthermore, we investigate the corresponding Toeplitz determinants for the logarithmic coefficients of the associated inverse functions. These sharp bounds are established for functions belonging to several well-known subclasses of $\mathcal{S}$, namely, the classes $\mathcal{S}^*(α)$ of starlike functions of order $α$, $\mathcal{C}(α)$ of convex functions of order $α$, $\mathcal{S}^*_α$ and $\mathcal{C}_α$ of strongly starlike and strongly convex functions of order $α$, and $\mathcal{R}(α)$ of functions with bounded turning. As special cases of our main results, we obtain the exact bounds of these determinants for the classical classes of starlike, convex, and bounded turning functions.

math.CV↗

arXiv2026

On some properties of logarithmic coefficients of inverse of univalent functions

In this paper we consider some properties of the initial logarithmic coefficients for inverse functions of functions univalent in the unit disc. The case of convex functions is treated separately. We give estimate, in some cases sharp, of the modulus of the initial coefficients, as well as the difference of the modulus of two consecutive coefficients.

math.CV↗

arXiv2026

On some properties of bi-univalent functions in the unit disc

In this paper we use a method based on the Grunsky coefficients to find upper bounds of the modulus of the initial coefficients, difference of the moduli of two consecutive initial coefficients, of the modulus of the initial logarithmic coefficient, and of the second Hankel determinant for the class of normalized bi-univalent functions.

math.CV↗