# Search: authors:"Paweł Zaprawa"

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#### 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...

#### Second Hankel Determinants for the Class of Typically Real Functions

November 2015; Revised 22 December 2015; Accepted 3 January 2016 Academic Editor: Marco Donatelli Copyright © 2016 Paweł Zaprawa. This is an open access article distributed under the Creative Commons

#### Second Hankel Determinants for the Class of Typically Real Functions

November 2015; Revised 22 December 2015; Accepted 3 January 2016 Academic Editor: Marco Donatelli Copyright © 2016 Paweł Zaprawa. This is an open access article distributed under the Creative Commons

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...