摘要
The conception of k_uniform smoothness (KUS) is introduced. It is the extension of the conception of uniform smoothness. It is proved that the k_uniform smoothness and Sullivan’s K_uniform rotundity (KUR) are the daul notions. X+* is a KUR space if and only if X is a KUS space, X+* is a KUS space if and only if X is a KUR space. If X is a KUS space, then X is a (K+1)US space. It is also proved that the KUS space includes the Nan’s k_strongly smooth space.
The conception ofk-uniform smoothness (KUS) is introduced. It is the extension of the conception of uniform smoothness. It is proved that thek-uniform smoothness and Sullivan’sK-uniform rotundity (KUR) are the daul notions. X* is a KUR space if and only if X is a KUS space, X* is a KUS space if and only if X is a KUR space. If X is a KUS space, then X is a (K + 1) US space. It is also proved that the KUS space includes the Nan’sk-strongly smooth space.
基金
themathematicalTianYuanfoundation,andbytheNaturalScienceFoundationofEducationCommitteeofInnerMongolia
