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On some generalization of local uniform smoothness and dual concepts

Suyalatu

Demonstratio Mathematica

2000

Vol. 33, nr 1

101-108

In this paper, the conception of local k-uniform smoothness (LkUS) is introduced on the base of the concept of k-uniform smoothness that introduced by Suyalatu and Wu Congxin. It is proved that the local k-uniform smoothness and Sullivan's local k-uniform rotundity (LkUR) are the dual notions. X is a LkUS space, then X is a L(k + 1)US space. However, the converse need not be true. In addition, we also obtain two important results about LkUS space.