Associated with the $L_p$-curvature image defined by Lutwak, some inequalities for extended mixed 𝑝-affine surface areas of convex bodies and the support functions of $L_p$-projection bodies are established. As a natural extension of a result due to Lutwak, an $L_p$-type affine isoperimetric inequality, whose special cases are $L_p$-Busemann–Petty centroid inequality and $L_p$-affine projection inequality, respectively, is established. Some $L_p$-mixed volume inequalities involving $L_p$-projection bodies are also established.
Volume 130, 2020
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