In this paper, we present a new subclass TΣ(μ)" role="presentation" >TΣ(μ) of bi univalent functions belong to Σ" role="presentation" >Σ in the open unit disc U={z:z∈Cand|z|<1}" role="presentation" >U={z:z∈Cand|z|<1}. Then, we use the concepts of Faber polynomial expansions to find upper bound for the general coefficient of such functions belongs to the defined class. Further, for the functions in this subclass we obtain bound on first three coefficients |a2|" role="presentation" >|a2|, |a3|" role="presentation" >|a3| and |a4|" role="presentation" >|a4|. We hope that this paper will inspire future researchers in applying our approach to other related problems.
In this paper, we present a new subclass TΣ(μ)" role="presentation" >TΣ(μ) of bi univalent functions belong to Σ" role="presentation" >Σ in the open unit disc U={z:z∈Cand|z|<1}" role="presentation" >U={z:z∈Cand|z|<1}. Then, we use the concepts of Faber polynomial expansions to find upper bound for the general coefficient of such functions belongs to the defined class. Further, for the functions in this subclass we obtain bound on first three coefficients |a2|" role="presentation" >|a2|, |a3|" role="presentation" >|a3| and |a4|" role="presentation" >|a4|. We hope that this paper will inspire future researchers in applying our approach to other related problems.
