Relations of a planar domains bounded by hyperbolas with families of holomorphic functions
Relations of a planar domains bounded by hyperbolas with families of holomorphic functions
Abstract We consider a family of analytic and normalized functions with the property that $zf'(z)/f(z)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>z</mml:mi> <mml:msup> <mml:mi>f</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mo>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>)</mml:mo> <mml:mo>/</mml:mo> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>)</mml:mo> </mml:math> (or $1+zf''(z)/f'(z)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>z</mml:mi> <mml:msup> <mml:mi>f</mml:mi> <mml:mo>″</mml:mo> </mml:msup> <mml:mo>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>)</mml:mo> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>f</mml:mi> <mml:mo>′</mml:mo> </mml:msup> …