渐近非扩张型映射的不动点定理

Fixed point theorems for mappings of asymptotically nonexpansive type

证明设X是具一致正规结构的Banach空间 ,C是X的非空有界子集 ,T :C→C是渐近非扩张型映射且存在某个N0 ∈N使得TN0 在C上连续 ,进一步设存在C的非空闭凸子集E具有性质 (P) ,则T在E中有不动点。

The purpose of this paper is to proof that Suppose X is a Banach space with uiform normal structure,C is a nonempty bounded subset of X,and T:C→C is an asymptotically nonexpansive type mapping such that there exists N 0∈N such that T N 0 is continuous on C.Further,suppose that there exists a nonempty closed convex subset E of C with the following property(P): x∈E implies ω W(x)E where ω W(x) is the weak ω-limit set of T at x;that is ,the set {y∈X:y=weak - lim iT n i x for some n i↑∞} The T has a fixed point in E.