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Search: authors:"Paweł Zaprawa"

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Third Hankel Determinants for Subclasses of Univalent Functions

The main aim of this paper is to discuss the third Hankel determinants for three classes: \(S^*\) of starlike functions, \(\mathcal {K}\) of convex functions and \(\mathcal {R}\) of functions whose derivative has a positive real part. Moreover, the sharp results for twofold and threefold symmetric functions from these classes are obtained.

On Coefficients Problems for Typically Real Functions Related to Gegenbauer Polynomials

We solve problems concerning the coefficients of functions in the class \(\mathcal {T}(\lambda )\) of typically real functions associated with Gegenbauer polynomials. The main aim is to determine the estimates of two expressions: \(|a_4-a_2 a_3|\) and \(|a_2 a_4 -a_3{}^2|\). The second one is known as the second Hankel determinant. In order to obtain these bounds, we consider the...

Circularly Symmetric Locally Univalent Functions

Let \(D\subset \mathbb {C}\) and \(0\in D\). A set D is circularly symmetric if, for each \(\varrho \in \mathbb {R}^+\), a set \(D\cap \{\zeta \in \mathbb {C}:|\zeta |=\varrho \}\) is one of three forms: an empty set, a whole circle, a curve symmetric with respect to the real axis containing \(\varrho \). A function f analytic in the unit disk \(\Delta \equiv \{\zeta \in \mathbb...

Covering Problems for Functions \(n\) -Fold Symmetric and Convex in the Direction of the Real Axis II

Let \({\mathcal {F}}\) denote the class of all functions univalent in the unit disk \(\Delta \equiv \{\zeta \in {\mathbb {C}}\,:\,\left| \zeta \right| <1\}\) and convex in the direction of the real axis. The paper deals with the subclass \({\mathcal {F}}^{(n)}\) of these functions \(f\) which satisfy the property \(f(\varepsilon z)=\varepsilon f(z)\) for all \(z\in \Delta...