Galatia Cleanthous

Monotonicity theorems for analytic functions centered at infinity

We consider the family of analytic functions centered at infinity with Laurent expansion f(z) = cz + c0 + ∑∞ j=1 cjz −j . We prove some monotonicity theorems involving geometric quantities such as diameter, radius and length.

Multi-point bounds for analytic functions under measure conditions

Let be an analytic function on the unit disc with image satisfying a measure condition. We prove an upper and a lower bound for the modulus for every involving all the pre-images of