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

In this paper, we consider a class of normalized harmonic functions in the unit disk satisfying a third-order differential 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 harmonic polynomials involving Gaussian hypergeometric function which belong to the considered class. We also provide examples illustrating graphically with the help of Maple.

Automated summary

In this paper, a class of normalized harmonic functions in the unit disk satisfying a third-order differential inequality is considered, and various properties of this class are investigated. Harmonic polynomials involving Gaussian hypergeometric function belonging to this class are constructed as an application, with graphical examples provided using Maple software.