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J. Korean Math. Soc. 2014; 51(3): 567-592
Printed May 1, 2014
https://doi.org/10.4134/JKMS.2014.51.3.567
Copyright © The Korean Mathematical Society.
Construction of subclasses of univalent harmonic mappings
Sumit Nagpal and V. Ravichandran
University of Delhi, University of Delhi
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.
Keywords: univalent harmonic mappings, starlike, convex, close-to-convex, coefficient estimates, growth estimate, convolution, convex combination, integral operators
MSC numbers: Primary 31A05, Secondary 30C45
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