We introduce and solve 3-variable additive functional inequalities and prove the Hyers-Ulam stability of the 3-variable additive functional inequalities in complex Banach spaces. This is applied to investigate homomorphisms in C*-algebras, Lie C*-algebras and JC*-algebras, and derivations on C*-algebras, Lie C*-algebras and JC*-algebras associated with the 3-variable additive functional inequalities. Moreover, we study homomorphisms in C*-ternary algebras and C*-triple systems, and derivations C*-ternary algebras and C*-triple systems associated with the 3-variable additive functional inequalities.

Chun-Gil Park. He has accomplished his doctoral degree in Mathematics from the University of Maryland and is currently working as a professor at Hanyang University. He is working for several journals such as Journal of Nonlinear Science and Applications and Journal of Computational Analysis and Applications as the associate editors and Journal of Nonlinear Analysis and Applications as the Editor-in-Chief. His main research topics include operator algebras, functional inequalities, functional equations, non-commutative geometry, fixed point theory and fuzzy mappings. He has published a number of academic articles on international journals related to operator algebras, functional inequalities, functional equations, non-commutative geometry, fixed point theory and fuzzy mappings. Within the last twenty years, he has successfully published more than 500 articles on SCI-E journals.