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Motivated by the celebrated work of Lutwak, Yang and Zhang [ 1 ] on(p,q)\left(p,q)-mixed volumes and that of Feng and He [ 2 ] on(p,q)\left(p,q)-mixed geominimal surface areas, we in the present paper establish and confirm the affine isoperimetric and Brunn-Minkowski-type inequalities with respect to(p,q)\left(p,q)-mixed geominimal surface areas.

Isoperimetric and Brunn-Minkowski inequalities for the ( p , q )-mixed geominimal surface areas