Linear mappings approximately preserving [formula omitted]-orthogonality

Abstract

We define the concept of approximate ρ∗-orthogonality preserving mapping between normed linear spaces and give some characterizations for a linear mapping to be approximately ρ∗-orthogonality preserving. Moreover, we show that every approximately ρ∗-orthogonality preserving linear mapping is necessarily a scalar multiple of an almost isometry.