Geometric properties of $\log$-polyharmonic mappings

Abstract

In this paper, a class of $\log$-polyharmonic mappings ${\mathcal{L}}_p\mathcal{H}$ together with its subclass ${\mathcal{L}}_p\mathcal{H}(G)$ in the unit disk $\mathbb{D}=\{z:|z|<1\}$ is introduced, and several geometrical properties such as the starlikeness, convexity and univalence are investigated. In particular, we consider the Goodman-Saff conjecture and prove that the conjecture is true in ${\mathcal{L}}_p\mathcal{H}(G)$.

11 pages

References in corpus (1)

• On polyharmonic univalent mappings