Hilbert空间中κ-严格伪压缩的强收敛定理(英文)

Strong Convergence Theorem for κ-Strict Pseudo-Contractions in Hilbert Spaces

在无穷维Hilbert空间中,即使对非扩张映像Mann,迭代算法仅有弱收敛。为了得到强收敛定理,该文利用Hilbert空间中闭凸子集的一个序列和一个给定向量作适当的凸组合修改Mann迭代算法,在Hilbert空间中给出了一个新的κ-严格伪压缩修正的Mann迭代算法——似Ishikawa迭代算法,并且建立了该算法的强收敛定理。推广和改进了一些最新的结果。

In an infinite dimensional Hilbert space, the normal Mann＇s iterative algorithm has only weak convergence, in general, even for non-expansive mappings. In order to get a strong convergence result, the normal Mann＇s iterative algorithm is modified by using a suitable convex combination of a fixed vector and a sequence in a closed convex subset of a real Hilbert space. A strong convergence theorem is established by means of a new Ishikawa-like iterative algorithm for κ-strict pseudo-contractions in Hilbert spaces. The results presented in this paper have extended and improved some recent results.