On the Marx conjecture for the convex hulls of families of starlike and convex mappings
On the Marx conjecture for the convex hulls of families of starlike and convex mappings
We prove a Marx conjecture for the closed convex hull of the family of functions which are starlike of order <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="alpha"> <mml:semantics> <mml:mi>α<!-- α --></mml:mi> <mml:annotation encoding="application/x-tex">\alpha</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <italic>k</italic>-fold symmetric. We obtain precise results for the functions which are starlike, starlike of order …