A New Insight with Trigonometric Coefficients of Additive-Quadratic Functional Equations and its Stability Analysis

This study introduces a novel framework for analyzing the Ulam-Hyers stability of mixed-type additive-quadratic functional equations with trigonometric constant coefficients in Banach spaces. Employing advanced analytical techniques and leveraging the unique properties of trigonometric functions, we derive sufficient conditions for the stability of these equations. The intricate relationship between additive and quadratic components is rigorously examined, emphasizing the pivotal role of trigonometric coefficients in influencing stability behavior. Our results provide fresh insights into the structural stability of functional equations and broaden the scope of existing stability theories. This work lays the groundwork for future research on mixed-type functional equations in both theoretical and applied mathematical contexts