A New Approximate Birkhoff Orthogonality Type

Abstract

In this note, we introduce a new approximate Birkhoff orthogonality type and give a characterization for inner product spaces using the approximate orthogonality. We show some general properties of the approximate Birkhoff orthogonality type as well as applications. In particular, we study the relationship between the new approximate Birkhoff orthogonality type and other approximate orthogonality types that have been defined before. Furthermore we study the approximate preserving mapping and give some properties.