On Holomorphic Self-Maps of a Disk with Fixed Points

Key Points

• To derive Cowen and Pommerenke inequalities for holomorphic maps of a disk with fixed points using the Lindelof principle and capacity approach.
• Application of the Lindelof principle
• Utilization of the capacity approach
• Derivation of inequalities for holomorphic maps
• Demonstrated the Cowen and Pommerenke inequalities for holomorphic maps
• Generalizations of these inequalities for maps with fixed points were established