局部凸空间拟非扩张集值映射不动点定理

Fixed Point Theorems for Set-valued Mappings of Quasi-nonexpansive Type to Locally Convex Space

§1 引言 Husian和Tarafdar[1]在局部凸线性拓扑空间内研究了非扩张型集值映射的不动点问题,推广了Browder定理[2]Kirk[3]等人的有名结果,本文讨论更一般的拟非扩张集值映射的不动点问题,并给出满足一定边界条件的拟非扩张非自映射的不动点定理。

In this paper a main result is obtained. Let X be a locally convex topological vector space, E a nonempty, weakly compact,convex subset of X which posses normal structure. Let T be a multivalued mapping of E in-to 2~E. If for any α∈I. x,y∈E, u∈Tx, v_k∈T^ky, p_α(u-v_1)=sup(p(x-v_k))here k≥0 andv_0=y.then there exist x_0∈E such that Tx_0=(x_0).