Certain geometric properties of close-to-convex harmonic mappings

In this talk, we discuss a family of sense-preserving harmonic mappings whose analytic part is convex in one direction. We prove that functions in this family are close-to-convex for certain values of parameters. Also, we discuss bounds on pre-Schwarzian derivatives and bounds on the Bloch’s constant. In addition, we discuss the coefficient estimates, growth and distortion results.