A generalization of Study’s theorem on convex maps
A generalization of Study’s theorem on convex maps
Study proved that disks of radius <italic>r</italic>, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="0 greater-than r less-than-or-slanted-equals 1"> <mml:semantics> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>></mml:mo> <mml:mi>r</mml:mi> <mml:mo>⩽<!-- ⩽ --></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">0 > r \leqslant 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, get mapped onto convex (starlike) sets under all convex (starlike) maps of the unit disk …