Lower Schwarz–pick Estimates and Angular Deirivatives

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-type Estimates Forthe Hyperbolic Derivative

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...

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

Greedy and Randomized Versions of the Multiplicative Schwarz Method

We consider sequential, i.e., Gauss-Seidel type, subspace correction methods for the iterative solution of symmetric positive definite variational problems, where the order of subspace correction steps is not deterministically fixed as in standard multiplicative Schwarz methods. Here, we greedily choose the subspace with the largest (or at least a relatively large) residual norm for the next up...