Construction of close-to-convex harmonic polynomials

Abstract

A family of sense–preserving complex valued harmonic polynomials that are close-to-convex on the open unit disk is introduced. By taking limits as the degree of the polynomials tends to infinity, a famiiy of close-to-convex harmonic mappings is also obtained. Similar results are considered for mappings of the punctured disk.

Keywords:

• Harmonic mapping
• Close-to-convex
• Univalent

1991 Mathematics Subject Classification:

• Primary, 30C45