Generalized Schwarz-Pick estimates

Schwarz-pick-type Estimates Forthe Hyperbolic Derivative

Lower Schwarz–pick Estimates and Angular Deirivatives

The well-known Schwarz–Pick lemma states that any analytic mapping φ of the unit disk U into itself satisfies the inequality |φ′(z)| ≤ 1− |φ(z)| 2 1− |z|2 , z ∈ U. This estimate remains the same if we restrict ourselves to univalent mappings. The lower estimate is |φ′(z)| ≥ 0 generally or |φ′(z)| > 0 for univalent functions. To make the lower estimate nontrivial we consider univalent functions ...

A ug 2 00 6 LOWER SCHWARZ - PICK ESTIMATES AND ANGULAR DERIVATIVES

The well-known Schwarz-Pick lemma states that any analytic mapping φ of the unit disk U into itself satisfies the inequality |φ ′ (z)| ≤ 1 − |φ(z)| 2 1 − |z| 2 , z ∈ U. This estimate remains the same if we restrict ourselves to univalent map-pings. The lower estimate is |φ ′ (z)| ≥ 0 generally or |φ ′ (z)| > 0 for univa-lent functions. To make the lower estimate non-trivial we consider univalen...

Schwarz-Pick Estimates for Holomorphic Mappings with Values in Homogeneous Ball

and Applied Analysis 3 Let K z, z be the Bergman kernel function. Then the Bergman metric Hz β, β can be defined as

The Schwarz – Pick theorem and its applications

Various derivative estimates for functions of exponential type in a half-plane are proved in this paper. The reader will also find a related result about functions analytic in a quadrant. In addition, the paper contains a result about functions analytic in a strip. Our main tool in this study is the Schwarz–Pick theorem from the geometric theory of functions. We also use the Phragmén–Lindelöf p...