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

Abstract

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 involve Gaussian hypergeometric function which belong to the considered class. We also provide examples illustrating graphically with the help of Maple.

Certain new subclass of close-to-convex harmonic functions defined by a third-order differential inequality

“…Very recently, Yaşar and Yalçın [10] defined the class R H 0 ( , ) G J of harmonic functions which satisfy the third-order differential inequality:…”

New subclass of the class of close-to-convex harmonic mappings defined by a third-order differential inequality

“…In all studies mentioned above [10,17,18,23], it is proved that the functions in corresponding classes are close-to-convex. Also, coefficient bounds, growth estimates, and convolution properties of the classes are obtained.…”

“…They constructed harmonic polynomials involving Gaussian hypergeometric function which belong to the class W 0 H (δ, λ) . Very recently, Yaşar and Yalçın [23]…”

New subclass of the class of close-to-convex harmonic mappings defined by a third-order differential inequality

“…In all studies mentioned above [15,8,16,21], it is proved that the functions in corresponding classes are close-to-convex. Also, coefficient bounds, growth esti-mates, and convolution properties of the classes are obtained.…”

“…They constructed harmonic polynomials involving Gaussian hypergeometric function which belong to the class W 0 H (δ, λ) . Very recently, Yaşar and Yalçın [21]…”