Initial coefficient estimates for a new subclasses of analytic and $m$-fold symmetric bi-univalent functions

Abbas Kareem Wanas 1 and Sibel Yalcın 2 *

doi:10.26637/MJM0703/0018

Initial coefficient estimates for a new subclasses of analytic and $m$-fold symmetric bi-univalent functions

Authors :

Abbas Kareem Wanas ¹ and Sibel Yalcın^{2 *}

Author Address :

¹ Department of Mathematics, College of Science, University of Al-Qadisiyah, Diwaniyah, Iraq.
² Department of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Bursa, Turkey.

*Corresponding author.

Abstract :

In the present investigation, we define two new subclasses of the function class $Sigma_{m}$ of analytic and $m$-fold symmetric bi-univalent functions defined in the open unit disk $U$. Furthermore, for functions in each of the subclasses introduced here, we determine the estimates on the initial coefficients $left| a_{m+1} ight|$ and $left| a_{2m+1} ight|$. Also, we indicate certain special cases for our results.

Keywords :

Analytic functions, univalent functions, bi-univalent functions, m-fold symmetric bi-univalent functions, coefficient estimates.

DOI :

10.26637/MJM0703/0018

Article Info :

Received : September 19, 2018; Accepted : February 06, 2019.