平面两凸域的Bonnesen型对称混合不等式

investigate the symmetric mixed isoperimetric deficit Δ2( K 0, K 1) of domains K 0 and K 1 in the Euclidean plane R 2 via the known kinematic formulas of Poincare and Blaschke in integral geometry. Then we obtain symmetric mixed isoperimetric inequality and some Bonnesen-style symmetric mixed inequalities. One of those inequalities strengthens Kotlyars inequality. Finally, we obtain some reverse Bonnesen-style symmetric mixed inequalities that generalize the known Bottemas result.