Robust Approximation and Stability of Highly Nonlinear Composite Additive–Quadratic Functional Equations in Various Banach Spaces

Abstract

In this groundbreaking paper, we pioneer the investigation of the generalized Ulam-Hyers-Rassias stability of a composite additive-quadratic functional equation in various Banach spaces, including Banach Space, Generalized 2 Banach space, and Random Banach Space. Leveraging the powerful classical Hyers and Radu's fixed point methods, we rigorously establish the stability results, thereby significantly advancing the frontiers of functional equation theory.