Open Access Research

Some properties of starlike harmonic mappings

Melike Aydog̃an1*, Arzu Yemisci2 and Yaşar Polatog̃lu2

Author Affiliations

1 Department of Mathematics, Işık University, Mesrutiyet Koyu, Sile Kampusu, 34980, Istanbul, Turkey

2 Department of Mathematics and Computer Science, Kültür University, E5 Freeway Bakirköy, 34156, Istanbul, Turkey

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Journal of Inequalities and Applications 2012, 2012:163 doi:10.1186/1029-242X-2012-163

Published: 23 July 2012

Abstract

A fundamental result of this paper shows that the transformation

<a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/163/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/163/mathml/M1">View MathML</a>

defines a function in <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/163/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/163/mathml/M2">View MathML</a> whenever <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/163/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/163/mathml/M3">View MathML</a> is <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/163/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/163/mathml/M2">View MathML</a>, and we will give an application of this fundamental result.

MSC: 30C45, 30C55.

Keywords:
harmonic starlike function; growth theorem; distortion theorem