Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2021; 36(4): 671-684

Online first article September 24, 2021      Printed October 31, 2021

https://doi.org/10.4134/CKMS.c200168

Copyright © The Korean Mathematical Society.

Hypergeometric distribution series and its application of certain class of analytic functions based on special functions

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