Exponential Powers of the Product of Two Univalent Log-Harmonic Mappings

Abstract

In this paper, we examine some classes of univalent λ-spirallike log-harmonic mappings defined on the unit disk. We present several sufficient conditions for two given $\lambda$-spirallike log-harmonic mappings, f_1(z) and f_2(z), which guarantee that exponential powers of their product, $F(z) = ( f_1(z) f_2(z) )^{e^{λ}}$, is a univalent starlike log-harmonic mapping.