On a subclass of close-to-convex harmonic mappings

In this paper, we introduce a new class of sense preserving harmonic mappings f = h + (g) over bar over bar in the open unit disk and prove that functions in this class are close-to-convex. We give some basic properties such as coefficient bounds, growth estimates, convolution and determine the radius of convexity for the sections of functions belonging to this family. In addition, we construct certain harmonic univalent polynomials belonging to this family.

Automated summary

This paper introduces a new class of sense-preserving harmonic mappings in the open unit disk and proves that functions in this class are close-to-convex. Basic properties such as coefficient bounds, growth estimates, and convolution are discussed, along with the determination of the radius of convexity for functions in this family. Additionally, certain harmonic univalent polynomials belonging to this family are constructed.