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A New Look for Starlike Logharmonic Mappings
Department of Mathematics, American University of Sharjah, Sharjah, UAE
- 1 Department of Mathematics, American University of Sharjah, Sharjah, UAE
Applied Mathematics·Volume 05 (2014)·Pages 1053–1060·Published 15 April 2014·DOI10.4236/am.2014.57099
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Abstract
A function f(z) defined on the unit disc U is said to be logharmonic if it is the solution of the nonlinear elliptic partial differential equation where such that . These mappings admit a global representation of the form where In this paper,we shall consider the logharmonic mappings , where is starlike. Distortion theorem and radius of starlikess are obtained. Moreover, we use star functions to determine the integral means for these mappings. An upper bound for the arclength is included.
KeywordsA New Look for Starlike Logharmonic Mappings
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