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

P. Gurusamy; M. Çağlar; S. Sivasubramanian; L. I. Cotirla

doi:10.3842/umzh.v76i7.7539

P. Gurusamy Department of Mathematics, Velammal Engineering College, Surapet, Chennai, India
M. Çağlar Department of Mathematics, Faculty of Science, Erzurum Technical University, Yakutiye, Turkey
S. Sivasubramanian Department of Mathematics, University College of Engineering Tindivanam, Anna University Tindivanam, India
L. I. Cotirla Department of Mathematics, Technical University of Cluj-Napoca, Romania

DOI: https://doi.org/10.3842/umzh.v76i7.7539

Keywords: Analytic functions, Univalent functions, prestarlike functions, Fekete-Szegö Inequality

Abstract

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.

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