Normality criterion for logharmonic mapping
Molla Basir Ahamed, Sanju Mandal
TL;DR
This paper establishes necessary and sufficient conditions for logharmonic mappings to be normal, extending classical criteria like Marty's, Zalcman-Pang, and Lohwater-Pommerenke theorems to this class of functions.
Contribution
It introduces new normality criteria for logharmonic mappings, including adaptations of classical theorems and an application of the Zalcman-Pang lemma.
Findings
Marty's criterion for logharmonic mappings
Zalcman-Pang lemma adapted for logharmonic functions
Lohwater-Pommerenke theorem for logharmonic mappings
Abstract
In this paper, we present several necessary and sufficient conditions for a logharmonic mapping to be normal i.e., we establish Marty's criterion, Zalcman-Pang lemma and the Lohwater-Pommerenke theorem for logharmonic mappings, along with an application of the Zalcman-Pang lemma.
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