Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality

Abstract

In this paper, we consider a class of normalized harmonic functions in the unit disk satisfying a third-orderdifferential inequality and we investigate several properties of this class such as close-to-convexity, coefficient bounds,growth estimates, sufficient coefficient condition, and convolution. Moreover, as an application, we construct harmonicpolynomials involving Gaussian hypergeometric function which belong to the considered class. We also provide examplesillustrating graphically with the help of Maple.