A new isoperimetric-type inequality and its stability

In this paper, we discuss the isoperimetric-type inequalities for the closed convex curve in the Euclidean plane R2. The main result of this paper is that we establish a family of para-metric inequalities. By adjusting the parameters, we can derive some well-known isoperimetric inequalities and some new improved isoperimetric-type inequalities. Furthermore, we investigate the stability property of the main inequality.