Convex hulls and extreme points of some families of univalent functions
Convex hulls and extreme points of some families of univalent functions
The closed convex hull and extreme points are obtained for the functions which are convex, starlike, and close-to-convex and in addition are real on<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis negative 1 comma 1 right-parenthesis"><mml:semantics><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mo>−<!-- − --></mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:annotation encoding="application/x-tex">( - 1,1)</mml:annotation></mml:semantics></mml:math></inline-formula>. We also obtain this result for the functions which are convex …