On New Convex Bodies and Reverse Bonnesen-Style, Inequalities in the Plane

Key words: 
• convex body，support function，new convex body，isoperimetric inequality，reverse Bonnesen-style inequality /
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Abstract: In this paper ,we have constructed three new classes of convex bodies by the support function of the given convex body .By discussing the geometric properties of the first two classes of convex bodies ,we have obtained some reverse Bonnesen‐style inequalities .Via discussing the last class of convex bodies ,we give the process that the given convex body changes a disk ,and the perimeter of the new convex body has not changed ,the are of the new convex body has not decreased in the process .