Research on geometric structures of Banach and function spaces with application of their [psi]-direct sums

刻画了有限多个Banach空间的[psi]-直和的弱近一致光滑性，引入了一类在Cn上产生偏[ell]_1范数的凸函数.作为应用，通过构造这样的凸函数，我们给出了许多非一致非平方非扩张映象的具有不动点性质的Banach空间，引入了一个与光滑模有关的几何常数A(X)，得到了一系列的结果，并且关于C2上的绝对范数的von Neumann-Jordan常数得到了一个结果，其中包含了几个前人的结果.

We characterized the weak nearly uniform smoothness of [psi]-direct sums of finitely many Banach spaces, where we introduced a class of convex functions which yield partial [ell]_1 norms on Cn. As an application, by constructing such a convex funtion we presented a plenty of Banach spaces with the fixed point property for nonexpansive mappings which are not uniformly non-square.We introduced a geometric constant A(X) which is connected to the modulus of smoothness and obtained a sequence of results, and also concerning the von Neumann-Jordan constant of absolute norms on C2 we obtained a result which contains a couple of previous results.