Initial Coefficient Bounds for a General Class of Bi-Univalent Functions

Abstract

Recently, Srivastava et al. <cite>HMS-AKM-PG</cite> reviewed the study of coefficient problems for bi-univalent functions. Inspired by the pioneering work of Srivastava et al. <cite>HMS-AKM-PG</cite>, there has been triggering interest to study the coefficient problems for the different subclasses of bi-univalent functions (see, for example, <cite>Ali-Ravi-Ma-Mina-class,Caglar-Orhan,BAF-MKA,Goyal-Goswami,Xu-HMS-AML,Xu-HMS-AMC</cite>,). Motivated essentially by the aforementioned works, in this paper we propose to investigate the coefficient estimates for a general class of analytic and bi-univalent functions. Also, we obtain estimates on the coefficients |a₂| and |a₃| for functions in this new class. Further, we discuss some interesting remarks, corollaries and applications of the results presented here.