L p -mixed intersection bodies

In this paper the author first introduce a new concept of L (p) -dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of L (p) intersection body to L (p) -mixed intersection body. Inequalities for L (p) -dual mixed volumes of L (p) -mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities.