- Hacettepe Journal of Mathematics and Statistics
- Vol: 51 Issue: 1
- New subclass of the class of close-to-convex harmonic mappings defined by a third-order differential...
New subclass of the class of close-to-convex harmonic mappings defined by a third-order differential inequality
Authors : Serkan Çakmak, Elif Yaşar, Sibel Yalcin
Pages : 172-186
Doi:10.15672/hujms.922981
View : 16 | Download : 5
Publication Date : 2022-02-14
Article Type : Research
Abstract :In this paper, we introduce a new subclass of harmonic functions f = s + ¯ t f=s+t¯ in the open unit disk U = { z ∈ C : | z | < 1 } U={z∈C:|z|<1} satisfying ${\text{Re}}\left[ \gamma \mathfrak{s}^{\prime }(z)+\delta z\mathfrak{s}^{\prime \prime }(z)+\left( \frac{\delta -\gamma }{2}\right) z^{2}\mathfrak{s}^{\prime \prime \prime }\left( z\right) -\lambda \right]>\left \vert \gamma \mathfrak{t}^{\prime }(z)+\delta z\mathfrak{t}^{\prime\prime }(z)+\left( \frac{\delta -\gamma }{2}\right) z^{2}\mathfrak{t}^{\prime \prime \prime }\left( z\right) \right \vert,$ where 0 ≤ λ < γ ≤ δ , z ∈ U . 0≤λ<γ≤δ,z∈U. We determine several properties of this class such as close-to-convexity, coefficient bounds, and growth estimates. We also prove that this class is closed under convex combination and convolution of its members. Furthermore, we investigate the properties of fully starlikeness and fully convexity of the class.Keywords : harmonic, univalent, close-to-convex, coefficient estimates, convolution