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 : 17 | Download : 3

Publication Date : 2022-02-14

Article Type : Research Paper

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 ${\text{Re}}\left[ \gamma \mathfrak{s}^{\prime }insert ignore into journalissuearticles values(z);+\delta z\mathfrak{s}^{\prime \prime }insert ignore into journalissuearticles values(z);+\leftinsert ignore into journalissuearticles values( \frac{\delta -\gamma }{2}\right); z^{2}\mathfrak{s}^{\prime \prime \prime }\leftinsert ignore into journalissuearticles values( z\right); -\lambda \right]>\left \vert \gamma \mathfrak{t}^{\prime }insert ignore into journalissuearticles values(z);+\delta z\mathfrak{t}^{\prime\prime }insert ignore into journalissuearticles values(z);+\leftinsert ignore into journalissuearticles values( \frac{\delta -\gamma }{2}\right); z^{2}\mathfrak{t}^{\prime \prime \prime }\leftinsert ignore into journalissuearticles values( z\right); \right \vert,$ 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