This study investigates univalent log-harmonic mappings, a class of functions that map the unit disk into the complex plane. First, we establish the necessary and sufficient conditions for univalent log-harmonic mappings to map the unit disk onto a spirallike region. We then explore the relationship between starlike harmonic mappings and spirallike log-harmonic mappings, providing several examples to illustrate our results. Finally, under specific conditions, we present growth and covering theorems for univalent log-harmonic mappings and determine the radius of spirallikeness for starlike log-harmonic mappings.
Citation: Chuang Wang, Junzhe Mo, Zhihong Liu. On univalent spirallike log-harmonic mappings[J]. AIMS Mathematics, 2024, 9(11): 30515-30528. doi: 10.3934/math.20241473
This study investigates univalent log-harmonic mappings, a class of functions that map the unit disk into the complex plane. First, we establish the necessary and sufficient conditions for univalent log-harmonic mappings to map the unit disk onto a spirallike region. We then explore the relationship between starlike harmonic mappings and spirallike log-harmonic mappings, providing several examples to illustrate our results. Finally, under specific conditions, we present growth and covering theorems for univalent log-harmonic mappings and determine the radius of spirallikeness for starlike log-harmonic mappings.
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Chuang Wang, Junzhe Mo, Zhihong Liu. On univalent spirallike log-harmonic mappings[J]. AIMS Mathematics, 2024, 9(11): 30515-30528. doi: 10.3934/math.20241473
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