Initial Maclaurin Coefficient Bounds for New Subclasses of Analytic and m-Fold Symmetric Bi-Univalent Functions Deﬁned by a Linear Combination

Hari M. Srivastava; Abbas Kareem Wanas∗

doi:10.5666/KMJ.2019.59.3.493

Article

KYUNGPOOK Math. J. 2019; 59(3): 493-503

Published online September 23, 2019

Initial Maclaurin Coefficient Bounds for New Subclasses of Analytic and m-Fold Symmetric Bi-Univalent Functions Deﬁned by a Linear Combination

Hari M. Srivastava, Abbas Kareem Wanas∗

Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China
e-mail : harimsri@math.uvic.ca
Department of Mathematics, College of Science, University of Al-Qadisiyah, Iraq
e-mail : abbas.kareem.w@qu.edu.iq

Received: December 7, 2018; Revised: March 19, 2019; Accepted: March 25, 2019

Abstract

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Abstract

In the present investigation, we define two new subclasses of analytic and m-fold symmetric bi-univalent functions defined by a linear combination in the open unit disk U. Furthermore, for functions in each of the subclasses introduced here, we establish upper bounds for the initial coefficients |a_m+1| and |a_2m+1|. Also, we indicate certain special cases for our results.

Keywords: analytic functions, univalent functions, m-Fold symmetric biunivalent functions, coefficient bounds.