Coefficient Bounds for a Subclass of Harmonic Mappings Convex in One Direction

Mohammad Mehdi Shabani; Maryam Yazdi; Saeed Hashemi Sababe

doi:10.5666/KMJ.2021.61.2.269

Article

Kyungpook Mathematical Journal 2021; 61(2): 269-278

Published online June 30, 2021

Coefficient Bounds for a Subclass of Harmonic Mappings Convex in One Direction

Mohammad Mehdi Shabani, Maryam Yazdi, Saeed Hashemi Sababe^*

Department of Mathematics, University of Shahrood, Shahrood, Iran
e-mail : Mohammadmehdishabani@yahoo.com

Young Researchers and Elite Club, Malard Branch, Islamic Azad University, Malard, Iran
e-mail : Msh_yazdi@yahoo.com

Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, and Young Researchers and Elite Club, Malard Branch, Islamic Azad University, Malard, Iran
e-mail : Hashemi_1365@yahoo.com and S.Hashemi@ualberta.ca

Received: August 6, 2020; Revised: December 14, 2020; Accepted: December 14, 2020

Abstract

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Abstract

In this paper, we investigate harmonic univalent functions convex in the direction 𝜃 , for 𝜃 ∈ [0,π) . We find bounds for |f_z(z)|, |fz¯(z)| and |f(z)|, as well as coefficient bounds on the series expansion of functions convex in a given direction.

Keywords: harmonic, univalent, convex, shear construction