Approximate of Homomorphisms and Derivations Structures in Normed Triple Lie Spaces

In this paper, we investigate the algebraic structures of homomorphisms and derivations, which play a significant role in the fields of physics and engineering sciences. The main focus of this study is on the perturbation of homomorphism and derivation structures associated with certain bidimensional Additive-Quadratic functional equation in normed triple Lie (3-Lie) systems, within the concept of Ulam-stability. By employing the fixed point theorem, we establish several required theorems, followed by specific and relevant corollaries that highlight the theoretical significance of our findings.