A Note on Convexity Properties for Gaussian Hypergeometric Function

Abstract

Gaussian hypergeometric function has been investigated in the context of geometric function theory regarding many aspects. Obtaining univalence conditions for this function is a line of research followed by many scholars. In the present study, methods specific to the differential superordination theory are used for obtaining properties of the Gaussian hypergeometric function regarding convexity of order . Also, a necessary and sufficient condition is proved such that Gaussian hypergeometric function is a close-to-convex function. The applicability of the theoretical findings is demonstrated by a numerical example.