Approximate norm‐additive maps on Banach spaces

Let be two Banach spaces, be an ‐norm‐additive map for some , that is, In this paper, we prove that if is surjective with , then there exists a linear surjective isometry such that The estimate is sharp. We also approximate standard surjective ‐norm‐additive maps between the positive cones of continuous function spaces by linear isometries within a sharp approximation error .