arXiv subjects
Publications and source records attributed to Şahsene Altınkaya.
We prove several formulas for the Hilbert metric in the unit disk and apply these results to study quasiregular mappings of the unit disk $\mathbb{B}^2$ onto a bounded convex domain $D$. The main result deals with the Hölder continuity of these mappings with respect to Hilbert metrics of $\mathbb{B}^2$ and $D$. Also several open problems are formulated.
The Mittag-Leffler function plays an important role in Geometric Function Theory, particularly in the study of analytic and meromorphic function classes. Among its various generalizations, the Barnes-Mittag-Leffler function stands out due to its intricate structure and applications in diverse mathematical fields. In this paper, our main focus is to investigate the convolution properties of these functions and establish conditions that ensure specific geometric characteristics. Additionally, we explore membership relations for functions in these classes. The results obtained in this work are novel, and their significance is demonstrated through various illustrative consequences and corollaries, emphasizing their potential impact in function theory and its applications.
For the error functions of the form \begin{equation*} E_{r}\mathfrak{f}(z)=\frac{\sqrt{πz}}{2}er\ \mathfrak{f}(\sqrt{z})=z+Σ_{n=2}^{\infty} \frac{(-1)^{n-1}}{(2n-1)(n-1)!}z^{n}, \end{equation*}% let $\mathcal{E}S_{\mathcal{H}}(k,λ,γ)\,$\ represent the class of harmonic error functions $\mathcal{ERF}=\mathcal{ERH}+\overline{\mathcal{% ERG}}$ in the open unit disk $\mathbb{U}=\left\{ z\in \mathbb{C}:\ \ \left\vert z\right\vert <1\right\} $. The paper attempts to present some basic properties for functions in this class.
In the present paper, we investigate connections between various subclasses of harmonic univalent functions by using a convolution operator involving the Pascal distribution series.
In this paper, we find the coefficient bounds using symmetric Toeplitz determinants for the functions belonging to the subclass $R(q)$.
In this work, we introduce two new subclasses S_{Σ_{m}}(α,λ) and S_{Σ_{m}}(\b{eta},λ) of Σ_{m} consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disk U. Furthermore, for functions in each of the subclasses introduced in this paper, we obtain the coefficient bounds for |a_{m+1}| and |a_{2m+1}|.