有限族严格伪压缩映象具误差的一类新的合成隐迭代程序

A Class of New Composite Implicit Iteration Process for Common Fixed Points of a Finite Family of Strictly Pseudocontractive Maps

参照强伪压缩映象不动点定理引进了涉及有限族严格伪压缩映象的带误差的合成隐迭代式.在实Banach空间框架下,利用Petryshyn不等式引理证明了该迭代序列强收敛于此严格伪压缩映象族的一个公共不动点.

In view of the existence theory for fixed point of a continuous pseudocontractive mapping, a new composite implicit iterative process with errors for a finite family of strictly pseudocontractive mappings is introduced reasonably in a real smooth Banach space. We have proved by means of the Petryshyn＇ s inequality that the iterative process converges strongly to a fixed point of the family of strictly pseudocontractive mappings under some suitable conditions.