Journal of the Korean Mathematical Society · 2014 · 27 citations · 23 references
Riemann-hilbert ProblemHarmonic Alexander OperatorQuasiconformal MappingFunction TheoryNew MethodologyFunctional AnalysisUnivalent Harmonic MappingsComplex Function TheoryHarmonic Space
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 notions of harmonic Alexander operator and harmonic Libera operator are introduced and their properties are investigated.
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