On harmonic bloch and normal functions

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Date

2005-08

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Publisher

Indian Nat Acad

Abstract

Let f = h + (g) over bar be a harmonic univalent and sense preserving function on the unit disk, where h and g are analytic. We give the definition of a normal harmonic function. The necessary and sufficient conditions for f = h + g to be Bloch or normal are determined. The sharp upper bound for vertical bar f (z) vertical bar is obtained whenever f = h + (g) over bar is a Bloch function. We obtain sharp estimates for the normality order of f when f maps the unit disk onto the unit disk.

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Keywords

Mathematics, Harmonic functions, Univalent functions, Bloch function, Normal function, Mappings

Citation

Öztürk, M. ve Yalçın, S. (2005). "On harmonic bloch and normal functions". Indian Journal of Pure and Applied Mathematics, 36(8), 407-416.