On a ρ-Orthogonally Additive Mappings

Abstract

We show that a real normed linear space endowed with the ρ-orthogonality relation, in general need not be an orthogonality space in the sense of R¨atz. However, we prove that ρ-orthogonally additive mappings defined on some classical Banach spaces have to be additive. Moreover, additivity (and approximate additivity) under the condition of an approximate orthogonality is considered.