Mohammed Y. Abed, Mahdi Dehghani, Ruhollah Jahanipur. Source: Annals of Functional Analysis, Volume 10, Number 4, 483--495.Abstract:
We introduce and study a generalized approximate orthogonality relation in real normed linear spaces, namely, approximate $\rho _{\lambda }^{v}$ -orthogonality. We investigate the relation between this generalized approximate orthogonality and approximate Birkhoff–James orthogonality. In particular, we show that every approximately $\rho _{\lambda }^{v}$ -orthogonality-preserving linear mapping is necessarily a scalar multiple of an almost isometry.