几何常数在不动点中的应用

The Application of Generalization Modulus of Convexity in Fixed Point Theory

讨论了各种几何常数与正规结构的关系，从而建立了几何常数与不动点性质之间的联系．进而讨论了广义凸性模α∈（0，1），广义凸性模（即函数δ^（α）（ε）：[0，2]→[0，1]）与benavides系数的关系得到了Banach空间具有一致正规结构的充分条件，从而得到了Banach空间上单值非扩张映射存在不动点的充分条件。

In this paper,we study the relations between geometric costant and normal structure. And we got the result between geometric constant and fixed points. First, we show the relations between generalized modulus of convexity and benavides condition that make the Banach space be coefficient and we conclude the sufficient uniform normal structure, and so we got the result that if a Banach space with the sufficient condition, the single value nonexpansive mapping in Banach space have fixed points.