In recent years, there has been a great interest in the study of additivity of mappings on rings as well as operator algebras (see  - , and references therein). Most of these results focus on the additivity of multiplicative maps, Jordan (triple) multiplicative maps, and Jordan elementary maps on rings, triangular algebras, and operator algebras. The first result in this direction is due to Martindale III who obtained the following pioneer result in 1969.
Jing, Wu and Lu, Fangyan, "Additivity Of Jordan (Triple) Derivations On Rings" (2011). Math and Computer Science Working Papers. 5.