Radius of starlikeness of convex combinations of univalent starlike functions
Radius of starlikeness of convex combinations of univalent starlike functions
The radius of starlikeness of the convex combination <disp-formula content-type="math/mathml"> \[ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="t f left-parenthesis z right-parenthesis plus left-parenthesis 1 minus t right-parenthesis g left-parenthesis z right-parenthesis comma 0 greater-than t greater-than 1 comma"> <mml:semantics> <mml:mrow> <mml:mi>t</mml:mi> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>+</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:mi>t</mml:mi> …