Lazarsfeld-Mukai reflexive sheaves and their stability

Consider an ample and globally generated line bundle L on a smooth projective variety X of dimension N≥2 over ℂ. Let D be a smooth divisor in the complete linear system of L. We construct reflexive sheaves on X by an elementary transformation of a trivial bundle on X along certain globally generated torsion-free sheaves on D. The dual reflexive sheaves are called the Lazarsfeld-Mukai reflexive sheaves. We prove the μL-(semi)stability of such reflexive sheaves under certain conditions.