We consider the Birkhoff-James orthogonality in normed spaces and classes of linear mappings exactly and approximately preserving this relation. Some related stability problems are posed.
"Remarks on orthogonality preserving mappings in normed spaces and some stability problems." Banach J. Math. Anal. 1 (1) 117 - 124, 2007. https://doi.org/10.15352/bjma/1240321561