OICC Press Mathematical Analysis and its Contemporary Applications 6 3 2024 09 01 Cauchy additive functional equation with quality and certainty of the approximation in generalized Z-numbers 10.30495/maca.2024.2031257.1103 EN Elumalai Sathya Department of Mathematics, Kalaignar Karunanidhi Government Arts College, Tiruvannamalai-606 603, TamilNadu, India Mohan Arun Kumar Department of Mathematics, Kalaignar Karunanidhi Government Arts College, Tiruvannamalai-606 603, TamilNadu, India Journal Article 2024 09 01 In this paper, we provide the generalized Ulam-Hyers stability of the Cauchy additive functional equation F(X + Y) = F(X) + F(Y) with quality and certainty of the approximation in generalized Z-numbers in the sense of Rassias and G˘avrut¸a.