Sharp coefficient inequalities and their applications for a class of analytic functions associated with an apple-shaped domain

In this study, we establish a novel subclass of analytic functions connected to bounded turning functions and governed by an apple-shaped domain. For this class, we estimate sharp coefficient bounds, evaluate the sharp Fekete-Szegö functional, and derive sharp Hankel determinants of the second and third orders. Our work contributes to geometric function theory, where analytic functions are studied to understand their behavior over specific domains. Such investigations, particularly involving coefficient inequalities, have significant applications in complex analysis (univalent functions and conformal mappings), engineering (fluid flow problems and signal processing) and mathematical physics (potential theory and quasi-conformal mappings). The sharpness of these bounds makes them particularly valuable for solving extremal problems in the aforementioned areas.