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.
Harmonic, univalent, close-to-convex, hypergeometric function
YAŞAR, ELİF and TOKGÖZ, SİBEL YALÇIN
"Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality,"
Turkish Journal of Mathematics: Vol. 45:
2, Article 5.
Available at: https://journals.tubitak.gov.tr/math/vol45/iss2/5