An analytical investigatıon on starlikeness and convexity properties for hypergeometric functions

Authors: İSMET YILDIZ, ALAATTİN AKYAR

Abstract: In this study, we analytically investigate hypergeometric functions having some properties such as convexity and starlike. We fundamentally focus on obtaining desired conditions on the parameters \(a,b\), and $c$ in order that a hypergeometric function to be in various subclasses of starlike and convex functions of order \(\alpha=2^{-r}\) and order \(\alpha=2^{-r}\) type $\beta=2^{-1}$, with $r$ is a positive integer.

Keywords: Analytic function, univalent function, starlike function, convex function, hypergeometric function, gamma function

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