Faber Polynomial Coefficient Estimates for Bi-Close-to-Convex Functions Defined by the <i>q</i>-Fractional Derivative

Abstract

By utilizing the concept of the q-fractional derivative operator and bi-close-to-convex functions, we define a new subclass of A, where the class A contains normalized analytic functions in the open unit disk E and is invariant or symmetric under rotation. First, using the Faber polynomial expansion (FPE) technique, we determine the lth coefficient bound for the functions contained within this class. We provide a further explanation for the first few coefficients of bi-close-to-convex functions defined by the q-fractional derivative. We also emphasize upon a few well-known outcomes of the major findings in this article.

Keywords

• quantum (or <i>q</i>-) calculus
• analytic functions
• <i>q</i>-derivative operator
• bi-univalent functions
• Faber polynomial expansions