Starlikeness of certain non-univalent functions
Starlikeness of certain non-univalent functions
Abstract We consider three classes of functions defined using the class $${\mathcal {P}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>P</mml:mi></mml:math> of all analytic functions $$p(z)=1+cz+\cdots $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>c</mml:mi><mml:mi>z</mml:mi><mml:mo>+</mml:mo><mml:mo>⋯</mml:mo></mml:mrow></mml:math> on the open unit disk having positive real part and study several radius problems for these classes. The first class consists of all normalized analytic functions f …