On the pre-Schwarzian norm of certain Logharmonic mappings
Md Firoz Ali, Sushil Pandit
TL;DR
This paper explores the properties of the pre-Schwarzian norm in logharmonic mappings, establishing conditions for finiteness, Bloch property, and growth behavior, linking it to analytic functions.
Contribution
It introduces new conditions connecting the pre-Schwarzian norm of logharmonic mappings to analytic functions and characterizes Bloch logharmonic functions.
Findings
Conditions for finite pre-Schwarzian norm in logharmonic mappings
Characterization of Bloch logharmonic functions
Growth estimates for logharmonic Bloch mappings
Abstract
We connect the pre-Schwarzian norm of logharmonic mappings to the pre-Schwarzian norm of an analytic function and establish some necessary and sufficient conditions under which locally univalent logharmonic mappings have a finite pre-Schwarzian norm. We also obtain a necessary and sufficient condition for a logharmonic function to be Bloch. Furthermore, we obtain the pre-Schwarzian norm and growth theorem for logharmonic Bloch mappings and their analytic and co-analytic parts.
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Taxonomy
TopicsMeromorphic and Entire Functions · Analytic and geometric function theory · Holomorphic and Operator Theory