Abstract: In this paper, the concepts of the ith L_p-mixed affine surface area and L_p-polar curvature images are introduced, some new inequalities connecting these new notions with L_p-centroid bodies and p-Blaschke bodies are showed. Moreover, a Blaschke-Santaio type inequality for L_p-mixed affine surface area is established. Our results also imply the similar to the inequalities for Marcus-Lopes, Bergstrom and Ky Fan.

Key words: L_p-mixed affine surface area, L_p-polar curvature images, p-Blaschke linear combination, L_p-centroid body