On univalent spirallike log-harmonic mappings

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.