Some New Applications of the Faber Polynomial Expansion Method for Generalized Bi-Subordinate Functions of Complex Order <i>γ</i> Defined by <i>q</i>-Calculus

Abstract

This work examines a new subclass of generalized bi-subordinate functions of complex order γ connected to the q-difference operator. We obtain the upper bounds ρm for generalized bi-subordinate functions of complex order γ using the Faber polynomial expansion technique. Additionally, we find coefficient bounds ρ2 and Feke–Sezgo problems ρ3−ρ22 for the functions in the newly defined class, subject to gap series conditions. Using the Faber polynomial expansion method, we show some results that illustrate diverse uses of the Ruschewey q differential operator. The findings in this paper generalize those from previous efforts by a number of prior researchers.

Keywords

• quantum (or <i>q</i>-) calculus
• analytic functions
• univalent functions
• <i>q</i>-derivative operator
• convex functions
• starlike functions