Abstract
Some formulas for the volumes of s-Orlicz convex simplices with s>0 are established. The convex-concave degree is introduced and studied for an s-Orlicz convex hull in the n-dimensional Euclidean spaces. As applications, the Yang-Zhang type geometric inequalities concerning s-Orlicz convex simplices with 0<s≤1 are proved. Also, a generalized formula for the volumes of unit balls in the p-normed spaces with p>0 is presented.
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