STABLE CLOSE-TO-CONVEXITY AND RADIUS OF FULL CONVEXITY FOR SENSE-PRESERVING HARMONIC MAPPINGS

Abstract

Given a sense-preserving harmonic function defined in the open unit disk with its analytic part restricted to the class of starlike functions, several techniques are developed to construct stable close-to-convex harmonic mappings. Each technique is demonstrated through illustrations. Moreover, the radii of full convexity are computed for sense-preserving harmonic functions with the analytic part belonging to certain subclasses of univalent functions. The obtained bounds are sharp.