The Fekete–Szegö functional associated with $m$-th root transformation using conical domains

• Дата: 2024
• Автори: Gurusamy, P., Çağlar, M., Sivasubramanian, S., Cotirla, L. I.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2024
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/7539
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 Let $\mathcal{A}$ be the class of analytic functions in the open unit disk  $\mathbb{U}=\{z\in \mathbb{C}\colon |z|<1\}.$  Let $\mathcal{R}_{\alpha }^{p}$ be the operator  defined on $\mathcal{A}$ by  \begin{equation*}\mathcal{R}_{\alpha }^{p}=f(z) \ast \frac{z}{{{{({1-z})}^{2({1-\alpha })}}}}.\end{equation*} A function $f$ in $\mathcal{A}$ is said to be in the class $k$-$\mathcal{SP}_{\alpha }^{p}$ if $\mathcal{R}_{\alpha }^{p}(f) $ is a $k$-parabolic starlike function.   We focus on the Fekete–Szegö inequality associated with $m$-th root transformation using conical domains for this class.