Jahangiri, Jay M. Harmonic functions starlike in the unit disk. (English) Zbl 0940.30003 J. Math. Anal. Appl. 235, No. 2, 470-477 (1999). An objective of this note is to study properties of sense preserving harmonic mappings \(f(z)= z+ a_2z^2+\cdots+ b_1\overline z+\cdots,|z|<1\) that satisfy the condition \({\partial\over\partial\theta} (\arg f'(re^{i\theta}))\geq \alpha\), \(0\leq\alpha< 1\), \(|z|= r\). Sufficient conditions (under some restrictions also necessary) are given and certain extremal questions are answered. Reviewer: E.Złotkiewicz (Lublin) Cited in 4 ReviewsCited in 52 Documents MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) Keywords:harmonic mappings PDF BibTeX XML Cite \textit{J. M. Jahangiri}, J. Math. Anal. Appl. 235, No. 2, 470--477 (1999; Zbl 0940.30003) Full Text: DOI References: [1] Avci, Y.; Zlotkiewicz, E., On harmonic univalent mappings, Ann. univ. mariae Curie-sklodowska sect. A, 44, 1-7, (1990) · Zbl 0780.30013 [2] Clunie, J.; Sheil-Small, T., Harmonic univalent functions, Ann. acad. aci. fenn. ser. A I math., 9, 3-25, (1984) · Zbl 0506.30007 [3] Duren, P.L., A survey of harmonic mappings in the plane, Texas tech. univ. math. ser., 18, 1-15, (1992) [4] Sheil-Small, T., Constants for planar harmonic mappings, J. London math. soc., 2, 237-248, (1990) · Zbl 0731.30012 [5] Silverman, H., Univalent functions with negative coefficients, Proc. amer. math. soc., 51, 109-116, (1975) · Zbl 0311.30007 [6] Silverman, H., Harmonic univalent functions with negative coefficients, J. math. anal. appl., 220, 283-289, (1998) · Zbl 0908.30013 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.