EXPLORING 𝗾-FIBONACCI NUMBERS IN GEOMETRIC FUNCTION THEORY: UNIVALENCE AND SHELL-LIKE CONVEX CURVES

Abstract

This paper presents a new subclass of convex functions associated with q-Fibonacci numbers, which is closely connected to shell-like starlike curves. Using the prin-ciple of subordination and exploiting the inherent properties of 𝗾-Fibonacci sequences, weperform a detailed investigation of the geometric and analytic features of this subclass. Inparticular, we identify the ranges of univalence and non-univalence for certain functions be-longing to this class and clarify their relationship with previously known families of convexfunctions.