On the properties of a class of polyharmonic functions

Abstract

The aim of this paper is to investigate some motivated geometrical aspects and properties of polyharmonic functions (PH) including starlikeness, convexity and univalence. A polyharmonicity preserving complex operator is also introduced. Further, a new subclass of polyharmonic functions (CPH) is defined and certain characteristics of elements of this subclass are examined and obtained. In particular, we extend Landau's theorem to functions in this subclass, and consider the Goodman–Saff conjecture and prove that the conjecture is true for mappings belonging to CPH.