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 Hypergeometric distribution series and its application of certain class of analytic functions based on special functions Commun. Korean Math. Soc. 2021 Vol. 36, No. 4, 671-684 https://doi.org/10.4134/CKMS.c200168Published online September 24, 2021Printed October 31, 2021 Gangadharan Murugusundaramoorthy, Saurabh Porwal Vellore Institute of Technology (Deemed to be University); Ram Sahai Government Degree College Abstract : The tenacity of the current paper is to find connections between various subclasses of analytic univalent functions by applying certain convolution operator involving generalized hypergeometric distribution series. To be more specific, we examine such connections with the classes of analytic univalent functions $k-\mathcal{UCV}^{*}\left( \beta \right)$, $k-\mathcal{S}_p^{*}\left( \beta \right)$, $\mathcal{R}\left( \beta \right)$, $\mathcal{R}^{\tau}(A,B)$, $k-\mathcal{PUCV}^{*}\left( \beta \right)$ and $k -\mathcal{PS}_p^{*}\left( \beta \right)$ in the open unit disc $\mathbb{U}$. Keywords : Analytic, univalent functions, uniformly convex functions, uniformly starlike functions, generalized hypergeometric function MSC numbers : Primary 30C45 Downloads: Full-text PDF   Full-text HTML

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