带误差项的广义Halpern-Ishikawa型迭代序列的强收敛定理

Generalized Halpern-Ishikawa type iterative sequences with error term strong convergence theorem

在实Banach空间中,为证明Φ-伪压缩映象不动点的迭代强收敛性,引进了带误差项的广义Halpern-Ishikawa型迭代算法,并利用所设计的迭代算法,证明了Φ-伪压缩映象不动点的一个新的强收敛定理。从而完善了带误差项的广义Halpern-Ishikawa型迭代算法的研究。

In the real Banach space,in order to prove the iterative convergence of the fixed point of Φ-pseudocompression map,a generalized Halpern-Ishikawa type iterative algorithm with error term is introduced.Using this designed iterative algorithm,a new strong convergence theorem for points of the fixed point of Φ-pseudocompression map is proved and generalized,thus optimizing the research on generalized Halpern-Ishikana type iterative algorithm with error term.