Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate

In this paper, we use the Faber polynomial expansion to find upper bounds for | a n | ( n ≥ 3) coefficients of functions belong to classes <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mtable> <m:mtr> <m:mtd> <m:msubsup> <m:mi>H</m:mi> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mi>Σ</m:mi> </m:mrow> </m:msubsup> <m:mo>(</m:mo> <m:mi>λ</m:mi> <m:mo>,</m:mo> <m:mi>h</m:mi> <m:mo>)</m:mo> <m:mo>,</m:mo> <m:mspace /> <m:mi>S</m:mi> <m:msubsup> <m:mi>T</m:mi> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mi>Σ</m:mi> </m:mrow> </m:msubsup> <m:mo>(</m:mo> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>h</m:mi> <m:mo>)</m:mo> <m:mspace /> <m:mtext> and</m:mtext> <m:mspace /> <m:mspace /> <m:msubsup> <m:mi>M</m:mi> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mi>Σ</m:mi> </m:mrow> </m:msubsup> <m:mo>(</m:mo> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>h</m:mi> <m:mo>)</m:mo> </m:mtd> </m:mtr> </m:mtable> </m:math> array HqΣ(λ,h),\, STqΣ(α,h)\, and \,\,MqΣ(α,h) array which are defined by quasi-subordinations in the open unit disk 𝕌. Further, we generalize some of the previously published results.