Harmonic mappings with the fixed analytic part

Rajbala, Jugal K. Prajapat

Department of Mathematics, Central University of Rajasthan, Bandarsindri, Kishangarh-305817, Dist.-Ajmer, Rajasthan, India

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 pre-Schwarzian 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.

UDC: 517.54

MSC: 30C45, 30C80

Received: 29.07.2020
Revised: 16.12.2020
Accepted: 17.12.2020

Language: English

DOI: 10.15393/j3.art.2021.8850

Bibliographic databases:

•