Hyers–Ulam stability via local functional inequalities in quasi-β-Banach spaces and some applications

In this paper, we study the stability of specific local functional inequalities within quasi-[Formula: see text]-Banach spaces, focusing on mappings that satisfy modular concavity and bounded perturbations. The analysis establishes the existence and uniqueness of [Formula: see text]-linear mappings that approximate these functions. Furthermore, we apply these results to investigate the stability of Lie homomorphisms and Lie derivations in quasi-[Formula: see text]-Banach spaces.