In this paper, the reverse Bonnesen style inequalities for convex domain in the Euclidean plane $mathbb{R}^2$ are investigated. The Minkowski mixed convex set of two convex sets K and L is studied and some new geometric inequalities are obtained. From these inequalities obtained, some isoperimetric deficit upper limits, that is, the reverse Bonnesen style inequalities for convex domain K are obtained. These isoperimetric deficit upper limits obtained are more fundamental than the known results of Bottema ([5]) and Pleijel ([22]).