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arxiv: 1209.0075 · v1 · pith:4J6EC6CWnew · submitted 2012-09-01 · 🧮 math.CV

Construction of subclasses of univalent harmonic mappings

classification 🧮 math.CV
keywords harmonicunivalentfunctionsmappingssubclassesalexanderanalyticcertain
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Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent analytic functions. The notion of harmonic Alexander integral operator is introduced. Also, the radius of convexity for certain families of harmonic functions is determined.

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