HARMONIC MAPPINGS WITH THE FIXED ANALYTIC PART

Abstract

In this article, we consider a class of sense-preserving harmonic mappings whose analytic part is convex in one direction. We prove that functions in this class are close-to-convex for certain values of parameters. Further, we obtain bounds on preSchwarzian derivatives and bounds on the Bloch’s constant. Finally, we obtain coefficient bounds, growth and distortion results.

Keywords

• univalent harmonic mappings
• functions convex in one direction
• pre-schwarzian derivative
• bloch’s constant
• coefficient bound
• growth and distortion results