On the properties of a class of log-biharmonic functions

The aim of this work is to introduce and investigate a new class of log-biharmonic functions. Certain geometrically motivated properties and results concerning starlikeness, convexity and univalence of elements within this class versus the corresponding harmonic functions are obtained and discussed. In particular, we consider the Goodman–Saff conjecture and prove that the conjecture is true for the logarithms of functions belonging to this class.