The stability problem in the sense of Ulam has recently been introduced and studied in the context of locally convex cones, as demonstrated in [29, 30]. In this work, we investigate the stability of 3D Cauchy–Jensen type operators within the framework of locally convex cones. We establish new stability results that provide a deeper understanding of the behavior of these operators under perturbations. Our findings contribute to the theoretical advancement of Hyers–Ulam stability in locally convex cones and highlight the unique properties of 3D Cauchy–Jensen type operators in these settings. This study enriches the mathematical foundation of stability theory and offers fresh insights into the interplay between some operators and locally convex structures.
