Abstract
We introduce a new subclass M(α, β) of close-to-convex harmonic mappings in the unit disk, which originates from the work of P. Mocanu on univalent mappings. We also give coefficient estimates, and discuss the Fekete-Szegő problem, for this class of mappings. Furthermore, we consider growth, covering and area theorems of the class. In addition, we determine a disk |z| in which the partial sum sm,n(f)(z) is close-to-convex for each function of the class M(α, β). Finally, for certain values of the parameters α and β , we solve the radii problems related to starlikeness and convexity of functions of this class.
Original language | English |
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Pages (from-to) | 1627-1643 |
Number of pages | 17 |
Journal | Complex Variables and Elliptic Equations |
Volume | 61 |
Issue number | 12 |
DOIs | |
State | Published - 1 Dec 2016 |
Externally published | Yes |
Keywords
- Fekete–Szegő problem
- Harmonic mapping
- area theorem
- close-to-convex function
- coefficient estimate
- convex function
- covering theorem
- growth theorem
- partial sum
- starlike function