Journal of Academy  for Basic and Applied Science

مجـلة الأكاديمية للعلــوم الاسـاســية والتطبيقية

The Distortion in Conformal Mapping in Hyperbolic Geometry
Salem I. El-Gawi
:بتاريخ2/19/2016 12:00:00 AM    

Nehari-type inequalities for normalized univalent functions are combined with elementary monotonicity arguments to give quick and simple proofs for numerous sharp two-point distortion theorems for conformal maps. These inequalities are used to prove two theorems of sharp two-point distortion theorems for conformal maps from the unit disk into the unit disk equipped with hyperbolic geometry. Keywords: Distortion, Conformal maps, Unit disc, Sharp two-point, and hyperbolic geometry