Optimal problem for the $L_{p}$ mixed chord integral

Bin Chen; Chao Li; Weidong Wang

doi:10.4171/rsmup/193

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Optimal problem for the $L_{p}$ mixed chord integral

Bin Chen
Lanzhou University of Technology, P. R. China
Chao Li
Ningxia University, Yinchuan, P. R. China
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Weidong Wang
China Three Gorges University, Yichang, P. R. China

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Abstract

In this paper we investigate the optimal problem for the $L_{p}$ mixed chord integral. The existence of the $L_{p}$ chord integral–Petty bodies is established, and the $L_{p}$ geominimal chord integral is proposed and its properties, such as invariance under orthogonal matrices, homogeneity, isoperimetric-type inequalities and cyclic-type inequalities, which are provided as well.

Cite this article

Bin Chen, Chao Li, Weidong Wang, Optimal problem for the $L_{p}$ mixed chord integral. Rend. Sem. Mat. Univ. Padova (2026), published online first

DOI 10.4171/RSMUP/193