Geometric Properties of log-Polyharmonic Mappings

Abstract

Abstract. In this paper, a class of log-polyharmonic mappings L p H together with its subclass L p H(G) in the unit disk 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 L p H(G).