On a subclass of close-to-convex harmonic mappings. (English) Zbl 1345.31004
Summary: We introduce a new subclass \(\mathcal{M}(\alpha,\beta)\) 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 \(|z|<r\) in which the partial sum \(s_{m,n}(f)(z)\) is close-to-convex for each function of the class \(\mathcal{M}(\alpha,\beta)\). Finally, for certain values of the parameters \(\alpha\) and \(\beta\), we solve the radii problems related to starlikeness and convexity of functions of this class.
MSC:
| 31A05 | Harmonic, subharmonic, superharmonic functions in two dimensions |
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 30C50 | Coefficient problems for univalent and multivalent functions of one complex variable |
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