Application of a Generalized Balloon-Shaped Domain on Bi-Bounded Turning Functions (Contemporary Mathematics, 2025)
This study addresses the contemporary scholarly interest in analytic functions tailored for specific domains and functions within the unit disk. These functions hold significant relevance across diverse technological and scientific disciplines, including but not limited to electromagnetic theory, plasma physics, mathematical biology, and optics. We introduce a novel subclass of bi-univalent functions formed by the convolution of bounded turning functions and generalized balloon-shaped domains. Our primary focus is on the investigation of coefficient-related problems, encompassing the second Hankel determinant, the Fekete-Szegö inequality, and initial coefficient bounds. This research provides precise bounds for each of these analytical challenges. To validate our findings, rather than a comparative analysis with existing results, a method that may be subject to inaccuracies stemming from previous methodologies, we leverage the extremal function for this newly defined class to confirm the precise limits for the characteristics examined herein.
Keywords: univalent functions, generalized balloon-shaped, bi-bounded turning functions, Hankel determinant