严格伪压缩映像族隐格式迭代逼近不动点几何结果

Geometric results for implicit iteration process approximating common fixed points of strictly pseudocontractive mappings

对非线性算子迭代序列逼近不动点过程的几何结构进行研究,在提出并证明了一个H ilbert空间中收敛序列的钝角原理基础上,应用这个钝角原理研究了严格伪压缩映像族的隐格式迭代序列逼近公共不动点的几何结构.并证明了相应的钝角原理.这个钝角原理表述了严格伪压缩映像族的隐格式迭代序列逼近公共不动点时与公共不动点集形成了钝角关系.这个钝角关系是使用相应内积序列的上极限表示的.事实上这个钝角结果的表述形式也是一个几何变分不等式,迭代序列的极限点即是这个几何变分不等式的解.一方面这个钝角结果表述了严格伪压缩映像族公共不动点隐格式逼近的几何过程,另一方面,这个钝角结果自然是隐格式迭代序列逼近严格伪压缩映像族公共不动点的必要条件.

The purpose of this paper is to study the geometric structure of approximating process of the fixed points by iteration sequence for nonlinear mappings, first prove a obtuse angle principle of convergence sequence in Hilbert space, therefore, by this obtuse angle principle to study the geometric structure of approximating process of the common fixed points for strictly pseudocontractive mappings. The relevant obtuse angle principle is proved. This obtuse angle principle expresse the relationship between the iteration sequence and fixed points set of strictly pseudocontractive mappings and it is expressed by the superior limits of inner product sequence. In fact that, this obtuse angle principle is also a geometric variational inquality. The limit point of iteration process is the solution of this geometric variational inquality. On the one hand, this obtuse angle principle expresse the geometric process of approximation of implicit iteration sequence for strictly pseudocontractive mappings, on the other hand, it is also a necessary condition for the approximating process of common fixed points of strictly pseudocontractive mappings by implicit iteration process.