and let $ x, y \in \mathbb{X}. $ For $ \epsilon \in [0, 1), $ we say that $ y \in x^{+(\epsilon)} $if $ \| x+\lambda y \|\geq \sqrt[]{1-\epsilon^2}~\|x\|$ for all $\lambda \geq 0. $ Similarly, we say that $ y \in x^{-(\epsilon)} $if $ \| x+\lambda y \|\geq \sqrt[]{1-\epsilon^2}~\|x\|$ for all $\lambda \leq 0. $

Motivated by the result on rotund bounded linear operators, we finally obtain a complete characterization of Birkhoff- James orthogonality of bounded linear operators on general normed linear spaces. As an application of the results obtained by us, we completely characterize Birkhoff-James orthogonality of bounded linear functionals on a normed linear space whose dual is strictly convex.

The study of the geometry of the space of bounded linear operators on a general normed linear space $\mathbb{X}$ is far more complicated than that of the ground space $\mathbb{X}.$ The relation of Birkhoff-James orthogonality of bounded linear operators with that of some special elements of $\mathbb{X}$ has been used in [@PSG] to obtain a sufficient condition for smoothness of a bounded linear operator. Carrying on in this direction we here obtain separate necessary and sufficient conditions for smoothness of a bounded linear operator on a general normed 