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Construction of a certain class of harmonic close-to-convex functions associated with the Alexander integral transform. (English) Zbl 1038.30010
In this paper the authors make use of the Alexander integral transforms of some analytic functions on the unit disc, which are starlike or convex of order \(\alpha\in [0,1)\), to study the construction of sense-preserving, univalent, and close-to-convex harmonic functions.

MSC:
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C20 Conformal mappings of special domains
44A15 Special integral transforms (Legendre, Hilbert, etc.)
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[1] DOI: 10.2307/2007212 · JFM 45.0672.02 · doi:10.2307/2007212
[2] Clunie J., Ann. Acad. Sci Fenn. Ser. AI Math. 9 pp 3– (1984)
[3] Duren P. L., Univalent Functions, Grundlehren der Mathematishcen Wissenschaften. Bd. 259 (1983)
[4] DOI: 10.1155/S1048953302000023 · Zbl 0999.30010 · doi:10.1155/S1048953302000023
[5] DOI: 10.1090/S0002-9904-1936-06397-4 · Zbl 0015.15903 · doi:10.1090/S0002-9904-1936-06397-4
[6] Srivastava H. M., Current Topics in Analytic Function Theory (1992) · Zbl 0976.00007
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