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

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 gamma. We used the Faber polynomial expansion method to determine the upper bounds for the functions belonging to the newly defined class of complex order gamma. For the functions in the newly specified class, we further obtained coefficient bounds vertical bar rho(2)vertical bar and the Fekete-Szeg problem vertical bar rho(3) - rho(2)(2)vertical bar, both of which have been restricted by gap series. We demonstrate many applications of the symmetric Slgean q-differential operator using the Faber polynomial expansion technique. The findings in this paper generalize those from previous studies.