Estimates for the Coefficients of Subclasses Defined by the q-Babalola Convolution Operator of Bi-Univalent Functions Subordinate to the q-Fibonacci Analogue (European Journal of Pure and Applied Mathematics, 2025)
In this work, we introduce and investigate a new subclass of bi-univalent functions defined via the q-Babalola operator and the q-Fibonacci analogue. The q-Babalola operator generalizes classical convolution-type operators in the context of q-calculus, enabling the analysis of geometric properties of analytic functions under quantum calculus frameworks. Meanwhile,the q-Fibonacci analogue extends the classical Fibonacci sequence into the realm of q-theory, offering new structural insights and recursive behavior in analytic function theory. For functions in this subclass, we derive sharp coefficient bounds for the initial Taylor coefficients |a2| and |a3|. Furthermore, we address the Fekete-Szeg ̈o functional problem associated with this class. Theinterplay between q-calculus and bi-univalent function theory revealed through our approach yields several novel and significant results, enriching the geometric function theory literature with new analytical tools and perspectives.
Keywords: Analytic function, Bi-univalent function, Starlike class, Fibonacci sequence, \(\q\)-calculus, Shell-like curves, Fekete-Szego functional, Babalola convolution operator