Von Neumann Publishing House Inc.Functional Analysis: Theory, Methods Applications(FATMA)ISSN 2371-13964120180706ε-continuity in the Hyers–Ulam–Rassias stability15ENSeyed Mohammad Sadeg Nabavi SalesDepartment of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, IranWe improve the well-known Hyers–Ulam–Rassias stability of the linear mappings in Banach spaces of Th.M. Rassias, by relaxing the assumption of continuity. We also state some results concerned with the stability of ε-continuous functionshttp://vonneumann-publishing.com/fatma/155/download-e-continuity-in-the-hyersulamrassias-stability