Certain New Applications of Faber Polynomial Expansion for a New Class of bi-Univalent Functions Associated with Symmetric q-Calculus

Abstract

In this study, we applied the ideas of subordination and the symmetric q-difference operator and then defined the novel class of bi-univalent functions of complex order γ. We used the Faber polynomial expansion method to determine the upper bounds for the functions belonging to the newly defined class of complex order γ. For the functions in the newly specified class, we further obtained coefficient bounds ρ2 and the Fekete–Szegő problem ρ3−ρ22, both of which have been restricted by gap series. We demonstrate many applications of the symmetric Sălăgean q-differential operator using the Faber polynomial expansion technique. The findings in this paper generalize those from previous studies.

Keywords

• symmetric q-calculus
• Faber polynomial expansion
• q-convex functions
• q-starlike functions
• symmetric q-derivative operator
• analytic functions