Shephard type problems for general $L_{p}$-centroid bodies.

Lutwak and Zhang proposed the concept of $L_{p}$-centroid bodies. Then Feng and Wang gave the notion of general $L_{p}$-centroid bodies. In this article, based on the $L_{p}$-dual affine surface area, we address Shephard type problems for the general $L_{p}$-centroid bodies. [ABSTRACT FROM AUTHOR]